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[Title]
205_

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% Ȃ΁C[Level1]ɏ̂̂܂ܖ蕶ƂȂB
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% vZߒꍇ́CƉ𓚂̊ԂɂPsԊuC
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[Level1]
Pʂ̕ϊ
$15km$̋𕪑$120m$ŐiނƂɂ鎞Ԃ͉ԉH

process
$\displaystyle \frac{15000(m)}{120(m/)}=125()=2()5()$

$2()5()$

$80kmő鎩Ԃ́C230ɉkmiނH$

process
$80(km/h) \times 2.5(h)=200(km)$

$200(km)$

$900km$ŔԃW{WFbg@B̃WFbg@$3.6$ԔԂƁC$km$iނH

process
$900(km/h) \times 3.6(h)=3240(km)$

$3240(km)$

900kmŔԃW{WFbg@B̃WFbg@͕̑bmH

process
$1=60=60\times 60b=3600b$ \\
\begin{eqnarray*}
 900(km/h) &=& \displaystyle \frac{900(km)}{3600(s)}=\frac{1}{4}(km/s)\\
 &=& 0.25(km/s)=250(m/s)
\end{eqnarray*}

$250(m/s)$

$40km$̎Ԃ15ƁiAj$km$i݂܂B

process
$15=\displaystyle \frac{1}{4}$B
$40\left[ \displaystyle \frac{km}{}\right]\times \displaystyle \frac{1}{4} \left[  \right]=10km$

$10km$

$40km$̎Ԃ45ƁiAj$km$i݂܂B

process
$45=\displaystyle \frac{3}{4}$B
$40\left[ \displaystyle \frac{km}{}\right]\times \displaystyle \frac{3}{4} \left[  \right]=30km$

$30km$

$6.4km$𕪑$40m$ŐiނƁiAjԁiCj܂B

process
$6400m \div 40 \left[ \displaystyle \frac{m}{}\right]=160=240$

$240$

$2.7km$͕iAj$m$łB

process
$2.7\left[ \displaystyle \frac{km}{} \right]
=\displaystyle \frac{2700 m }{60}=45\left[ \displaystyle \frac{m}{} \right]$

$45m$

$35m$͎iAj$km$łB

process
$35 \left[ \displaystyle \frac{m}{} \right] \times 60[]=2100m$

$2.1km$

b10m͎kmB

process
$\displaystyle \frac{10m}{1s}=\displaystyle \frac{3600\times 10\,m}{3600s}
=\displaystyle \frac{36km}{1}$

36km

60km͕mB

process
$\displaystyle \frac{60km}{1}=\displaystyle \frac{60000m}{60}
=\displaystyle \frac{1000m}{1}$

1000m

40km̗Ԃ3Ԃő鋗͉kmB

process
${\rm 40kkm/l\times 3kԁl=120kkml}$

120km

60km̎]Ԃ120km𑖂̂ɂ鎞Ԃ͉ԂB

process
${\rm 120kkml\div 60kkm/l=2kԁl}$

2

Ԃ72őĂ܂B̎Ԃ͉̕kmłB

process
$\displaystyle\frac{\rm 72kkml}{\rm 1kԁl}=\displaystyle\frac{\rm 72kkml}{\rm 60kl}=1.2kkm/l$

1.2km

300mőĂl܂B̐l̕b͉młB

process
$\displaystyle\frac{\rm 300kml}{\rm 60 ksl}=5km/sl$

b5m

Pn_Qn_܂ł̋12kmłB鎩Ԃ́CPQԂ30őIB
̎ԂPQԂ̕ς͉̑km/hH

process
$\displaystyle\frac{{\rm 12kkml}}{30kl}=\displaystyle\frac{{\rm 12kkml}}{0.5kԁl}=24$kkm/hl

$24kkm/hl$

̓ƂēK؂Ȃ̂C\textcircled{\small 1}$\sim$
\textcircled{\small 5}̒IыLœȂB\\
An_Bn_̊Ԃ𕪑150m̑ŉƂC
840bBACBn_̊Ԃ͉̓̂mB\\
\textcircled{\small 1}\,$1080$m~~~
\textcircled{\small 2}\,$1260$m~~~
\textcircled{\small 3}\,$1300$m\\
\textcircled{\small 4}\,$1680$m~~~
\textcircled{\small 5}\,̑

process
40b$=\displaystyle\frac{40}{60}$$=\displaystyle\frac{2}{3}$\\
840b$=8+\displaystyle\frac{2}{3}$$=\displaystyle\frac{26}{3}$\\
̂$150m/ \times \displaystyle\frac{26}{3}=1300$m

\textcircled{\small 3}









[Level2]
ς̑
n_Aƒn_B̊$48$kms͎$12$kmŐi݁CA͎$8$kmŐi݂܂B
̎̉̕ς͎̑iAjkmłB

process
s̎$=48\div 12=4$ԁCA̎$=48\div 8=6$\\
ς̑$=\displaystyle \frac{48 \times 2}{10}=9.6$

9.6

n_Aƒn_B̊$120$ms͕$30$mŐi݁CA͕$60$mŐi݂܂B
̎̉̕ς͕̑iAjmłB

process
s̎$=120\div 30=4$CA̎$=120\div 60=2$\\
ς̑$=\displaystyle \frac{120 \times 2}{6}=40$

$40$

n_Aƒn_B̊$120$ms͕$30$mŐi݁CA͕$50$mŐi݂܂B
̎̉̕ς͕̑iAjmłB

process
s̎$=120\div 30=4$CA̎$=120\div 50=2.4$\\
ς̑$=\displaystyle \frac{120 \times 2}{6.4}=37.5$

$37.5$

n_Aƒn_B̊Ԃs͕$600$mŐi݁CA͕$400$mŐi݂܂B
̎̉̕ς͕̑iAjmłB

process
$600$$400$̍ŏ{$1200$𓹂̂ƂƁC
s̎$=1200\div 600=2$CA̎$=1200\div 400=3$\\
ς̑$=\displaystyle \frac{1200 \times 2}{5}=480$

$480$

Ԃŉ܂Bs͖$40$kmCA͖$60$kmłB
ς͖̑${\rm km}$łB

process
4060̍ŏ{120kmГ̓̂ƂƁC\\
Ŝł$=3+2=5$ԁB\\
ς̑$=\displaystyle \frac{240}{5}=48$

$48$km

Ԃŉ܂Bs͖$20$kmCA͖$60$kmłB
ς͖̑${\rm km}$łB

process
2060̍ŏ{60kmГ̓̂ƂƁC\\
Ŝł$=3+1=4$ԁB\\
ς̑$=\displaystyle \frac{120}{4}=30$

$30$km

$21$km̋܂Bs͎$3$kmŕCA͎$7$kmő܂B
̂Ƃ̉̕ς͎̑iAjkmłB

process
Ŝ̋$21km \times 2=42$kmB
s̎Ԃ$7$CA̎Ԃ$3$Ȃ̂ŁCŜ̎Ԃ$10$B
ς̑$42 \div 10=4.2km$

$4.2km$

An_Bn_̂ɁCs͕$80m$CA͕$120m$Ői݂܂B
̕ς͕̑$m$łB

process
80120̍ŏ{240ABԂ̓̂ƂčlB
Ŝ̋$240 \times 2=480m$B
s̎Ԃ$3$CA̎Ԃ$2$Ȃ̂ŁCŜ̎Ԃ$5$B
ς̑$480 \div 5=96m$

$96m$

Г$14km$̓̂ɍs3ԁCA4Ԃ܂B
ς͎̑iAj$km$łB

process
Ŝ̋$28km$B
Ŝ̎Ԃ7ԂȂ̂ŁCς̑$\displaystyle\frac{28km}{7h} =4km$B

$4km$

$18km$̓̂ɍs͎$4km$CA͎$6km$Ői݂܂B
ς͎̑iAj$km$ɂȂ܂B

process
Ŝ̋$36km$B
sɂ鎞Ԃ$\displaystyle \frac{18}{4}=4.5$ԁBAɂ鎞Ԃ$\displaystyle \frac{18}{6}=3$ԂCŜ̎Ԃ$7.5$ԁB
ς̑\\
$36 \div 7.5=36 \times \displaystyle \frac{10}{75}
=12 \times \displaystyle \frac{2}{5}=12 \times \displaystyle \frac{4}{10}=4.8$

$4.8km$

sɎ$4km$̑$45$Đi񂾋CA͎$2.4km$Ői݂܂B
ς͎̑iAj$km$ɂȂ܂B

process
sɂ鎞Ԃ$\displaystyle \frac{3}{4}$\\
Aɂ鎞Ԃ
$3 \div 2.4=3 \times \displaystyle \frac{10}{24}=\displaystyle \frac{5}{4}$B\\
Cs̋$4 km/ \times \displaystyle \frac{3}{4}=3km$B
Ŝ̋$6km$BŜ̎Ԃ$2$ԁBς̑$6 \div 2=3km$B

$3km$

A͉wÕfp[g܂ōs͕$40m$CA͕$60m$ŉ܂B
ς͕̑$m$łB

process
4060̍ŏ{120ƂčlƁCs3CA2̂ŁCŜ̎Ԃ5B
ς̑$240 \div 5=48m$

$48m$

30km2Ԑi݁CɎ60km1Ԑi񂾂Ƃ̕ς̑߂B

process
30km2ԂC$30km\times 2=60km$iށB
60km1ԂC$60km\times 1=60km$iށB
$\displaystyle\frac{60+60}{2+1}=\displaystyle \frac{120}{3}=40km/$

40km

͂߂͎6km2ԕCɎ3km1ԕB̎̕ώ͉kmB

process
Ŝŕ̂\\
$6 \times 2+3 \times 1=15$km\\
ŜłԂ́C
$2+1=3$ԁB

5km

Ԃł͂߂͎40km3ԑCɎ50km2ԑB
̎̕ώ͉kmB

process
Ŝő̂́C\\
$40 \times 3+50 \times 2=220$km\\
ŜłԂ$3+2=5$ԁB\\
ώ
$\displaystyle\frac{\rm 220kkml}{\rm 5khl}=44kkm/hl$

44kkml

͂߂͕100m15Cɕ120m10B̎̕ϕ͉mB

process
Ŝŕ́C\\
$100 \times 15+120 \times 10=2700$mB\\
ŜłԂ́C\\
$15+10=25$B\\
߂镽ϕ\\
$\displaystyle\frac{2700}{25}=108$m

108m/

͂߂͕100m20Cɕ80m30B̎̕ϕ͉mB

process
ŜŐi񂾋́C\\
$100\times 20+80 \times 30=4400$m\\
ŜłԂ́C\\
$20+30=50$B\\
߂鑬́C
$\displaystyle\frac{4400}{50}=88$m/

88m/

1200mꂽ̂̂ɁCs͕100mŕCA͕150mőB
̕ϕ͉mB

process
̋$=2400$m\\
Ŝł$=12+8=20$\\
ϕ$\displaystyle\frac{2400}{20}=120$m/

120m/

An_Bn_܂ŕГ12km铹̂s͎6kmC
A͎4kmŕB̕ς͎̑kmB

process
sɂԂ2ԁCAɂԂ3ԁBāCς̑́C\\
$\displaystyle\frac{24 km}{5}=4.8$km

4.8km

1.5kmꂽƉŵɁCs͎3km/CA͎5km/ŕB̕ώ߂B

process
sɁC$1.5\div 3=0.5$ԁCAɁC$1.5\div 5=0.3$Ԃ邩C\\
$(1.5 \times 2)\div(0.5+0.3)=3\div 0.8=3\times \displaystyle\frac{5}{4}=3\times 1.25\\
=3.75$km/

3.75km/

Pn_Qn_܂12km铹̂s͎6kmCA͎4 kmŕB̕ς͎̑kmB

process
Ŝ̋$24km$B
sɂ鎞Ԃ$\displaystyle \frac{12}{6}=2$ԁBAɂ鎞Ԃ$\displaystyle \frac{12}{4}=3$ԂCŜ̎Ԃ$5$ԁB
ς̑\\
$24 \div 5=4.8$

$4.8km$

Ƃw܂120ms͕30mŐi݁CA͕60mŐi݂܂B
̎̉̕ς͕̑mB

process
Ŝ̋$240$mB
sɂ鎞Ԃ$\displaystyle \frac{120}{30}=4$BAɂ鎞Ԃ$\displaystyle \frac{120}{60}=2$CŜ̎Ԃ$6$B
ς̑\\
$240\div 6=40$

$40$m

Ƃw܂ōs͕300mŐi݁CA͕200mŐi݂܂B
̎̉̕ς͕̑mB

process
300200̍ŏ{600Ƃw܂ł̋ƂčlƁC
sɂ鎞Ԃ$\displaystyle \frac{600}{300}=2$BAɂ鎞Ԃ$\displaystyle \frac{600}{200}=3$CŜ̎Ԃ$5$B
ς̑\\
$1200\div 5=240$

240m

Г12kms͎6kmCA4kmŕƁC̕ώ͉kmB

process
s̎Ԃ$12\div 6=2$ԁCA̎Ԃ$12\div 4=3$ԁB
āCς̑$24\div 5=4.8$km/

4.8km

900m̋C͂300m܂ŕ60mCc𕪑80mŕƁCϕ͉mB

process
O̎Ԃ$300 \div 60=5$C㔼̎Ԃ$600 \div 80=\displaystyle\frac{15}{2}$B
āCς̑$900 \div \left(5+\displaystyle\frac{15}{2}\right)=900 \div \displaystyle\frac{25}{2}$

72m

1800m̎R͖30mC͖150mŕƁCς͕̑mB

process
̎Ԃ$1800 \div 30=60$C̎Ԃ$1800 \div 150=12$B
ς̑$1800 \times 2\div 72=50$

50m








[Level3]
Ԃɒ
ln_XY̊ԂCs͖6kmCA͖4km̑ŕC2ԂB
XY̊Ԃ̋͂炩B

process
߂鋗$x$ƂƁC \\
$\displaystyle \frac{x}{6}+\frac{x}{4}=2@2x+3x=24$ \\
$x=\displaystyle \frac{24}{5}=4.8(km)$

$4.8(km)$

ln_XY̊ԂCs͖6kmCA͖3km̑ŕC2ԂB
XY̊Ԃ̋͂炩B

process
߂鋗$x$ƂƁC \\
$\displaystyle \frac{x}{6}+\frac{x}{3}=2@x+2x=12$ \\
$x=\displaystyle \frac{12}{3}=4(km)$

$4(km)$

$15km$̓̂Cŏ̒n_rPn_܂ł͎$4km$ŕCPn_͎$6km$ŕƂC
Ŝ$3$ԂBŏ̒n_Pn_܂ł͉̋$km$łH

process
ŏ̒n_Pn_܂ł̋$x$ƂƁC\\
$\displaystyle \frac{x}{4}+\displaystyle \frac{15-x}{6}=3$

$6km$

AN̓}EeoCNŎR̂ӂƂR܂ł܂B
s͎$5km$œoCA͎$15km$ŉCS6Ԃ܂B
R̂ӂƂR܂ŉ$km$܂B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/205_/pic12.tex}
\end{center}
߂鋗$x$Ƃ΁C\\
$\displaystyle \frac{x}{5}+\displaystyle \frac{x}{15}=6$\\
$x=6 \times \displaystyle \frac{15}{4}=\displaystyle \frac{45}{2}=22.5$

$22.5km$

An_Bn_܂Bs͎$5km$Ői݁CA͎$20km$Ői񂾂ƂCS2Ԃ܂B
ABԂ͉̋kmłB

process
ABԂ̋$x \, km$ƂƁCs̎Ԃ$\displaystyle \frac{x}{5}$CA̎Ԃ$\displaystyle \frac{x}{20}$
ł邩C$\displaystyle \frac{x}{5}+\displaystyle \frac{x}{20}=2$B$\displaystyle \frac{5x}{20}=2$B
$x=8$

$8km$

AB܂ŉ̂ɁCH͎12kmōsC
H͎16kmŖ߂ƂCԂ330B
AB܂ł͉̋kmB

process
߂鋗$x$ƂƁC\\
$\displaystyle \frac{x}{12}+\displaystyle\frac{x}{16}=3\,\displaystyle\frac{1}{2}$

24km

lUs瓻14kmꂽKs֍ŝ3ԂB
Us瓻܂ł͎4kmCKs܂ł͎6km̑ōsƂB
Us瓻܂ł̓̂߂ȂB

process
߂铹̂$x$kmƂƁC\\
$\displaystyle\frac{x}{4}+\displaystyle\frac{14-x}{6}=3$\\
ӂ12ƁC\\
$3x+2(14-x)=36$
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/205_/pic14.tex}
\end{center}

8km

120km
ꂽړIn܂ŁC
ŏ͎ԂŎ50kmŐi݁CrŎ]Ԃɏ芷Ď20km
ړInɌƂ3ԂB]ԂŐi񂾋͉kmB

process
$\displaystyle\frac{120-x}{50}+\displaystyle\frac{x}{20}=3$\\
$2(120-x)+5x=300$\\
$x=20$km

20km
















[Level4]
Z
Ð̑10km̑DC5km̑ŗĂ܂B
̐D60km̂ɁCԂ܂B

process
D̉̑$=(D̐Ð̑+̗̑)$\\
̑D̉̑$10+5=15km/$\\
Ԃ$60\div 15=4$

4

Ð̑12km̑D6km̑ŗĂ܂B
̐30km̂ɉԂ܂B

process
D̏̑$=(D̐Ð̑-̗̑)$\\
̑D̏̑$12-6=6km/$\\
Ԃ$30 \div 6=5$

5

Ð̑10km̑DC5km̑ŗĂ܂B
̐CD60km̂ɉԂ܂B

process
$60\div(10+5)=60 \div 15=4$

4

Ð̑12km̑DC4km̑ŗĂ܂B
2Ԍɂ͉kmĂ܂B

process
$(12+4)\times 2=32km$

32km

DC5km̑ŗĂƁC2Ԍ24km̒ɂ܂B
̑D̐Ð̑߂ȂB

process
Ð̑$x\,km/$ƂƁC
$5+x=\displaystyle \frac{24}{2}$\\
$x=7$

$7$km

Ð̑12km̑DC6km̑ŗĂ܂B
̐30km̂ɁCԂ܂B

process
$30 \div(12-6)=5$

5

Ð̑8km̑DC5km̑ŗĂC2ԏ܂B
D̈ړ߂ȂB

process
$(8-5)\times 2=6$km

6km

DC6km̑ŗĂƁC2Ԍɂ4km̒ɓ܂B
̑D̐Ð̑߂ȂB

process
Ð̑$V\,km/$ƂƁC\\
$V-6= \displaystyle \frac{4}{2}$C$V=8km/$

8km

Ð̑10km̑DC3Ԍɂ6km̒ɂǂ܂B
̂Ƃ̗̐̑߂ȂB

process
̗̑$v\,km/$ƂƁC\\
$10-v=\displaystyle \frac{6}{3}$C$v=8km/$

8km

D16km̂2ԁC24km̂6Ԃ܂B
̑D̐Ð̑Ɛ̗̑ꂼꋁ߂ȂB

process
Ð̑$V$C̗$v$ƂƁC\\
$V+v=\displaystyle \frac{16}{2}$\\
$V-v=\displaystyle \frac{24}{6}$\\
̘AāC$V=6,\,v=2$

Ð̑$=6km$C\\
̗̑$=2km$

̂10kmDB
5ԁC1ԂƂƁC̑D̗̂ȂƂiނƂ̑ƁC
̗̑߂ȂB

process
Ð̑$V\,km/$C̗̑$v\,km/$ƂƁC\\
$V-v=\displaystyle \frac{10}{5}$\\
$V+v=\displaystyle \frac{10}{1}$\\
̘AāC$V=6,\,v=4$

Ð̑$=6km/$C\\
̗̑$=4km/$

Xn_̉Yn_CXYԂ30kmłB
܂C̗2km/łB
Ð𖈎20km/ő{[gŁCYn_Xn_ɍŝɉԂ邩B

process
Ƃ̑$(20-2)$km/B\\
$\displaystyle \frac{30}{18}=1\cdot\displaystyle \frac{12}{18}=1\cdot\displaystyle\frac{2}{3}$\\
$\displaystyle\frac{2}{3}=\displaystyle\frac{2}{3}\times 60=40$

140

ɉAB̊ԂDCɂ7ԁCɂ3ԂB
ABƂ̋42km̂ƂC̗͎kmB

process
Ð̑$V$kmC̗$v$kmƂƁC\\
$V-v=42 \div 7=6$\\
$V+v=42 \div 3=8$\\
$V=7,\,v=1$

1km

A_30kmɂB_܂őDŉB
4ԁC6ԂB
̗͎kmB

process
D̐Ð̑$V$kmC̗$v$kmƂƁC\\
$V+v=30 \div 4=7.5$\\
$V-v=30 \div 6=5$\\
$V=6.25,\,v=1.25$

1.25km







[Level5]
p
$44$km̓̂Cŏ$27$km͖$6$kmŁC$13$km͖$5.2$kmŁCc𖈎$4$kmŕB
ς͎̑kmłB

process
$27 \div 6=4.5$C\\
$13 \div 5.2=130 \div 52=\displaystyle \frac{13 \times 10}{52}=2.5C
4 \div 4=1$C
$\displaystyle \frac{44}{4.5+2.5+1}=\displaystyle \frac{44}{8}=5.5$km/

$5.5km/$

An$4$kmꂽByn֍ŝɁC߂͖$60$m̑ŕC
xȂ肻Ȃ̂œr疈$85$m̑ŕC$50$BnɒB
ςĂ牽m܂B

process
$\displaystyle \frac{4000-x}{60}+\displaystyle \frac{x}{85}=50$\\
$\displaystyle \frac{4000-x}{5 \times 12}+\displaystyle \frac{x}{5 \times 17}=50$\\
$\displaystyle \frac{17(4000-x)+12x}{5 \times 12 \times 17}=50$\\
$x=3400$m

$3400$m

1̎R͂ABB
lAB܂ōŝɁC𖈎$3km$ C𖈎$4km$̑ŕāC
$315$BɒB
܂CA͏𖈎$2km$C𖈎$4km$̑ŕāC$4$ԂAɒB
AB܂ł͉̓̂$km$H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/205_/pic07.tex}
\end{center}
AR܂ł̋$x$[km]CRB܂ł̋$y$[km]ƂB\\
315$=3+\displaystyle \frac{15}{60}()=\displaystyle \frac{13}{4}()$ \\
$\displaystyle \frac{x}{3}+\displaystyle \frac{y}{4}=\displaystyle \frac{13}{4}$c(1) 
@$\displaystyle \frac{x}{4}+\displaystyle \frac{y}{2}=4$c(2) \\
(1)C(2)$x=6Cy=5@6+5=11(km)$

$11(km)$

n_Xƒn_Y̊Ԃ]Ԃŉ̂ɁC
s͖$50km$CA͖$40km$̑őCA̎Ԃ͍s̎Ԃ$36$B
̂ƂCsɂԂ͉ԉH

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/205_/pic04.tex}
\end{center}
߂鎞Ԃ$t$()ƂƁC\\
$50t=40(t+36)$ \\
$t=144ij=120+24()=224$

$224$

n_Xn_Y܂ōŝɁCZ͎]ԂŖ$12km$C͓kŖ$4km$̑ŁC
ɒn_XoƂCẐق3ԑn_YɒB
n_XY܂ł̋͂炩H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/205_/pic10.tex}
\end{center}
n_Xn_Y܂ł̋$x(km)$ƂƁC
$\displaystyle \frac{x}{12}+3=\displaystyle \frac{x}{4}@x+36=3x@x=18$

18km

kŒn_Xn_Y܂ōŝɁC$4km$ōsƗ\肵Ԃ$15$C
$5km$ōsƗ\肵Ԃ$15$ZkB
n_XY̋͂炩H

process
\肵Ԃ$t$()ƂƁC\\
$4\left( t+\displaystyle \frac{1}{4} \right)=5\left(t-\displaystyle \frac{1}{4} \right)$ 
@$t=\displaystyle \frac{9}{4}()$ \\
n_XY̋́C\\
$4\left( \displaystyle \frac{9}{4}+\displaystyle \frac{1}{4} \right)=10(km)$

$10(km)$

Ƃ$2km$ꂽFB̉Ƃ֍ŝɁC͂߂͖$60m$̑ŕC
r̃Rrj̑O疈$80m$̑ŕC$30$ɗFB̉ƂɒB
ƂRrj܂ł̓̂߂ȂB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/205_/pic09.tex}
\end{center}
ƂRrj܂ł̋$x$ƂƁC\\
$\displaystyle \frac{x}{60}+ \frac{2000-x}{80}=30$ \\
iʁjƂRrj܂ł̎Ԃ$t$ƂƁC\\
$60t+80(30-t)=2000$ \\
$t=20@60 \times 20=1200m$

$1200(m)$

R̂ӂƂR܂Ŗ$30m$̑ŏC
R$1$ԋx񂾌CRӂƂ܂Ŗ$50m$̑ŉB
ɗvԂ͉ɗvԂ$20$B
̂ƂCӂƂR܂ł͉̋$km$H

process
iʁj\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/205_/pic11.tex}
\end{center}
ӂƂR܂ł̋$x$ƂƁC\\
$\displaystyle \frac{x}{30}=\displaystyle \frac{x}{50}+20$\\
ɗvԂ$t$()ƂƁC\\
$30(t+20)=50t@t=30()$ \\
$50 \times 30=1500(m)$

$1500(m)$

lS瓻z$15km$ꂽT֍sB
S瓻܂ł͖$3km$CT܂ł͖$5km$̑ŕāC$340$B
T܂ł̋͂炩H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/205_/pic08.tex}
\end{center}
$340=3+\displaystyle \frac{40}{60}=3+\displaystyle \frac{2}{3}=\displaystyle \frac{11}{3}()$ \\
߂鋗$x(km)$ƂƁC\\
$\displaystyle \frac{15-x}{3}+\displaystyle \frac{x}{5}=\displaystyle \frac{11}{3}$ \\
$x=10(km)$

$10(km)$

$2100m$ꂽwɍŝɁC͂߂͖$3.6km$̑ŕC
r疈$9km$̑ŕƂC$26$B̂ƂCԂ͉H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/205_/pic05.tex}
\end{center}
$3.6(km/h)=\displaystyle \frac{3600(m)}{60()}=60(m/)$ \\
$9(km/h)=\displaystyle \frac{9000(m)}{60()}=150(m/)$ \\
߂鎞Ԃ$t()$ƂƁC\\
$60t+150(26-t)=2100$ \\
$t=\displaystyle \frac{1800}{90}=20()$

$20()$

wZs܂ōŝɖ$4km$ŕĂ̂ƁC
$12km$Ŏ]ԂōŝƂł͂鎞Ԃ30ႤB
wZs܂ł͉̋$km$H

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/205_/pic06.tex}
\end{center}
wZs܂ł̋$x$ƂƁC
$\displaystyle \frac{x}{4}=\displaystyle \frac{x}{12}+\displaystyle \frac{1}{2}$\\
iʁj$30()=0.5(h)$BƂ̎Ԃ$t(h)$ƂƁC\\
$4(km/h) \times t(h)=12(km/h) \times (t-0.5)(h)$ \\
$t=\displaystyle \frac{3}{4}(h)@4(km/h) \times \displaystyle \frac{3}{4}(h)=3(km)$

$3(km)$

$24km$̋Cs͎$8km$ŁCA͎iAj$km$̑Ői񂾂ƂCς̑$6km$ɂȂ܂B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/205_/pic13.tex}
\end{center}
sɂԂ$24 \div 8=3$ԁB
Ȃ$x \, km$ƂƁCAɂԂ$\displaystyle \frac{24}{x}$ԁB
ӂC$3+\displaystyle \frac{24}{x}=\displaystyle \frac{48}{6}$B
$x=\displaystyle \frac{24}{5}=\displaystyle \frac{48}{10}=4.8$

$4.8km$

n_Aƒn_B̊Ԃ$1200$młBs͕$100$mŐi݁CA͕iAjmŐi݂܂B
̎̉̕ς͕̑$150$młB

process
s̎$=1200\div 100=12$CA̎Ԃ$x$ƂƁC\\
ς̑$=150=\displaystyle \frac{1200 \times 2}{12+x}$\\
$12+x=\displaystyle \frac{2400}{150}=16$C$x=4$\\
߂鑬$\displaystyle \frac{1200}{4}=300$

$300$

Ƃ1100mꂽw܂ōŏ͕70mŕC
r番150mőB
Ƃo10ȓɉwɒɂ́C
铹̂mȏɂ΂悢B\\
\textcircled{\small 1}\,$600m$~~~
\textcircled{\small 2}\,$650m$~~~
\textcircled{\small 3}\,$700m$~~~
\textcircled{\small 4}\,$750m$~~~
\textcircled{\small 5}\,$800m$

process
߂鋗$x [m]$ƂƁC\\
$\displaystyle\frac{1100-x}{70}+\displaystyle\frac{x}{150}\leqq 10$\\
$150(1100-x)+70x\leqq 70\times 150 \times 10$\\
$x\geqq \displaystyle\frac{6000}{8}=750$

\textcircled{\small 4}





[Level6]

[Level7]


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