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[Title]
206_lZCʉߎZ

% 蕶
% Ȃ΁C[Level1]ɏ̂̂܂ܖ蕶ƂȂB
[Problem]
̖₢ɓB
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% Level1̖BȉLevel7܂œlB
% 1sڂɂ͏ڍאݒ̃^CgB
% 2sڈȍ~ɖƂ̉𓚂B
% Ɖ𓚁C𓚂Ɩ͂PsďB
% vZߒꍇ́CƉ𓚂̊ԂɂPsԊuC
% ŏprocessƂsC̎̍svZߒĂB


[Level1]
Ε̗lZ
n_ABꂼꔽΕɏo܂B
Ȃ͖b2mCB͖̑b3mƂƁC40bɂ2l̓̂͂ǂꂾĂ܂B

process

1sԂ$(2+3)$m邩C$(2+3)\times 40=200$m

$200$m

R̊wZƎR̉w$600$mĂ܂B
AN͎R̊wZR̉w֖b$2$mŁCBN͎R̉wR̊wZ֖b$3$mŌ܂B
$2$l͉bɏo܂B

process
$600 \div (2+3)=120$s

$120$b

AB̉Ƃ2700mĂ܂BAB̉ƂցCBẢƂ֌ēɏoƂC
$20$ɏo܂B
Ȃ𖈕$60$mƂƁCB͖̑mɂȂ܂B

process
$\displaystyle \frac{2700}{20}=60+x$C$x=75$

$75$m

600m̒r̎CABn_瓯ɔΕɕn߂B
A͖50mCB͖70m̑ŕƂƁC
2lo̂͏oĂ牽ォB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic121.tex}
\end{center}
$\displaystyle\frac{600}{50+70}=\displaystyle\frac{600}{120}=5$

5

1200mꂽ2lꂼꖈ60mƖ40m̑ŋ߂ÂƂA
2l͉ɏoB

process
2l͖$60m+40m=100m$߂ÂĂ̂ŁA
$\displaystyle \frac{1200m}{100m/}=12$

12

1.2kmꂽꂼ̉ƂA͖50mCBN͖70m̑ł݂̉ƂɌĕB
2lo̂́CBN̉Ƃ牽m̒n_߂ȂB

process
BN݂ƁAAN
$50-(-70)=120$m/ŋ߂ÂB
2lo̂́A\\
$\displaystyle\frac{\rm 1200 m}{\rm 120 m/}=10$\\
$70\times 10=700$m
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic132.tex}
\end{center}

700m

A͎6kmCB͎4kmŐi݂܂B
ŏAB́i A jkmꂽn_ɂ܂B
AB͌Đi񂾂̂ŁC3ԂAB͏o܂B

process
BAƑΑx$6-(-4)=10$km/ŋ߂ÂB
߂鋗$10\times 3=30$km

30km

20km̒r̂܂C6kmAƎ4kmB܂܂B
2lɓƂoCΕɂ܂܂B
2lo͉̂ԌłB

process
ɂȂ20km̂悤ɐiށB\\
A$\longrightarrow$ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$\longleftarrow$ B\\
---------------------------------------------------------\\
@\\
BA݂ƑΑx$6-(-4)=10$km/ŋ߂ÂB߂鎞Ԃ
$20\div 10=2$

2










[Level2]
̗lZ
n_ABɁCA͖b$3$mCB͖b$2$m̑ŏo܂B
$40$bɂ́C$2$l̓̂͂ǂꂾĂ܂B

process
B݂A͖b$(3-2)$m̑C\\
$(3-2) \times 40=40$m

$40$m

AB́CʂĎRoĂ܂B
$2$l̑A$20$mCB$45$mŁCAB̂傤$500$mOĂƂłB
B́CƉAɒǂ܂B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic101.tex}
\end{center}
A݂B͕$(45-20)$mŋ߂ÂC\\
$500 \div 25=20$

$20$

͕$45$m̑ŏo܂B
킪oĂ$20$ɌZ̖YꕨɋCtCǂCiǂĂj$30$ɒɒǂ܂B
Z͕̑młB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic102.tex}
\end{center}
Z̑$x\,m/$ƂB
킩݂ƌZ\\
$(x-45)\,m/$ŋ߂Â\\
$(45 \times 20)\div 30=x-45$C$x=75$

$75\,$m/

͂$800$mr̎CZƒ킪CɓꏊoCɐi݂܂B
10CZ1x̒ɒǂ܂B
Z̑𖈕$250$mƂƁC͖̑młB
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic103.tex}
\end{center}

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic104.tex}
\end{center}
̑𖈕$x$\,mƂB킩猩ƌZ͖$(250-x)$mŋ߂ÂB
$250-x=\displaystyle \frac{800}{10}$

$170$m

600m̒r̎CABn_瓯ɓɕn߂B
A͖50mCB͖70m̑ŕƂƁC
2lĂяo̂͏oĂ牽ォB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic122.tex}
\end{center}
A݂B(70-50)=20m/̑ΓIȑŕĂB
āC\\
$\displaystyle \frac{600}{20}=30$

30

100mɖ60mŐiA𖈕100mBǂB
ɒǂB

process
A݂B$100-60=40$m/ŋ߂ÂA\\
$\displaystyle \frac{100m}{40m/}=2.5$

2.5

$70m$̑ŕĉƂoB
ƂoĂ$4$ɁC]ԂŖ$210m$̑ŖǂB
ɒǂ̂́CƂoĂ牽ォH

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic02.tex}
\end{center}
͉ƂoĂ$4$C$70(m/) \times 4()=280(m)$iłB
̋C݂̑Αx$210-70=140(m/)$ŒǂƁC
$280(m) \div 140(m/)=2()$ \\
iʁjƂoĂCɒǂ܂ł̎Ԃ$t$[]ƂƁC\\
$210t=70(4+t)@t=\displaystyle \frac{280}{140}=2()$

$2()$

$70m$̑ŕĉƂoB
ƂoĂ$6$ɁC]ԂŖ$210m$̑ŖǂB
ɒǂ̂́CƂoĂ牽ォH

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic01.tex}
\end{center}
͉ƂoĂ$6$C$70(m/) \times 6()=420(m)$iłB
̋C݂̑Αx$210-70=140(m/)$ŒǂƁC
$420(m) \div 140(m/)=3()$ \\
iʁjƂoĂCɒǂ܂ł̎Ԃ$t$[]ƂƁC\\
$210t=70(6+t)@t=\displaystyle \frac{420}{140}=3()$

$3$()

$70m$̑ŕĉƂoB
ƂoĂ$8$ɁC]ԂŖ$210m$̑ŖǂB
ɒǂ̂́CƂoĂ牽ォH

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic03.tex}
\end{center}
͉ƂoĂ$8$C$70(m/) \times 8()=560(m)$iłB
̋C݂̑Αx$210-70=140(m/)$ŒǂƁC
$560(m) \div 140(m/)=4()$ \\
iʁjƂoĂCɒǂ܂ł̎Ԃ$t$[]ƂƁC\\
$210t=70(8+t)@t=\displaystyle \frac{560}{140}=4()$

$4$()

A͎6kmCB͎4kmŐiށB
ŏAB5kmꂽn_ɂ܂B
ABɐiނƂCA͉ԂBɒǂ܂B

process
BAƑΑx$6-4=2$km/ŋ߂ÂC߂鎞Ԃ\\
$5\div 2=2.5$

2.5












[Level3]
܂ԂlZ
$9km$ꂽ̉wƎR̉w}\܂B
A͕150mCB͕100mœɓ̉wo܂B
R̉w܂ԂĂABo̂́C2loĂ牽łB
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic105.tex}
\end{center}

process
߂鎞Ԃ$t$ƂB
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic105p.tex}
\end{center}
$(100+150)t=9000 \times 2$\\
$t=\displaystyle \frac{18000}{250}=72$

$72$

Z͕$70$mC$65$mœɉƂoCw܂ł̓܂B
Z͉wɒƂɈԂCoĂ$40$$2$l͏o܂B
Ƃw܂ŉkmĂ܂B
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic106.tex}
\end{center}

process
߂鎞Ԃ$t$ƂB
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic106p.tex}
\end{center}
$(70+65)\times 40=5400$m\\
$\displaystyle \frac{5400}{2}=2700$m

$2.7$km

ABɖkoC$3.6$kmꂽ쒬Ƃ̊Ԃ܂B
B͖̑$90$mŁCɓ쒬܂ԂĂAƁCoĂ$36$ɏo܂B
Ȃ͕młB
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic107.tex}
\end{center}

process
߂鑬$x$ƂB
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic107p.tex}
\end{center}
$(x+90)\times 36=3600 \times 2$m\\
$x+90=\displaystyle \frac{3600 \times 2}{36}=200$m

$110$m/














[Level4]
ʉߎZ
$200$m̗ԂCdԂʉ߂̂$12$b܂B
̗Ԃ͕̑bmłB

process
$(200+100) \div 12=25$m/b

$25$m/b

$100$m̗ԂC$200$m̓Sʉ߂̂$12$b܂B
̗Ԃ͕̑bmłB

process
$200 \div 10=20$m/b

$20$m/b

$100$m̗ԂC$200$m̃glʉ߂̂$12$b܂B
̗Ԃ͖̑bmłB

process
$(200+100) \div 12=25$

b$25$m/b

$200$m̗ԂCb$25$m̑őĂ܂B
̗ԂC$150$m̓Sʉ߂̂ɉb܂B

process
$(150+200) \div 25=14$

$14$b

ԂC100m̉w̃z[ʉ߂̂ɁC6b܂B
Ԃ͖̑b28młB
Ԃ͉̒młB

process
$100+x=28 \times 6$

68m

$100$m̗ԂC$400$m̃glɂĎpȂԂ$15$błB
̗Ԃ͕̑bmłB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic108.tex}
\end{center}
$(400-100) \div 15=20$

b$20$m

80m̗Ԃb20mőĂ܂B
400m̃glɂČȂԂ͉błB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic109.tex}
\end{center}
$(400-80) \div 20=16$

$16$b

160m̗ԂC840m̓Snn߂ĂCnI܂50bB
̗Ԃ͎̑kmB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic14.tex}
\end{center}
$840+160=1000m=1km$B
$50b=50b\times \displaystyle \frac{1}{3600b}=\displaystyle \frac{5}{360}$B\\
$=\displaystyle \frac{1km}{5/360()}=72(km/)$

72km

400m̃glɕb24mőԂĂ鎞Ԃ15błB
̗Ԃ͉̒mB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic110.tex}
\end{center}
$400-x=24 \times 15$

40m

80m̗Ԃb28mőĂ܂B
̗ԂglɊSɂĂ鎞Ԃ15błB
̃gl̒߂ȂB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic111.tex}
\end{center}
$x-80=28 \times 15$

500m

Ԃ̒300m̓SAʉ߂̂23bC
200m̓SBʉ߂̂18b܂B
̗Ԃ̕bƒ߂ȂB

process
Ԃ̑$v$ƂƁC\\
$300+x=23 \times v$c\textcircled{\small 1}\\
$200+x=18 \times v$c\textcircled{\small 2}\\
\textcircled{\small 2}$\times (-1)$F$-200-x=-18 \times v$c\textcircled{\small 2}$'$\\
\textcircled{\small 1}{\textcircled{\small 2}$':100=5v$C$v=20$C
$x=110$

b$20$mC110m

100m̓Sʉ߂̂10bԂ܂B
̗Ԃ350m̃glɊSɂĂ鎞Ԃ15błB
̗Ԃ̕bƒ߂B

process
Ԃ̑$v$C$x$mƂƁC\\
$100+x=10\times v$c\textcircled{\small 1}\\
$350-x=15\times v$c\textcircled{\small 2}\\

b18mC80m

150m̗Ԃ72kmőĂB
̗ԂC950m̃glɂĂglʂ蔲܂ŁCb܂B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic116.tex}
\end{center}
$\displaystyle \frac{72000m}{3600s}=20m/s$\\
$\displaystyle \frac{950+150}{20}=55s$

55b

63kmőĂԂ330mglɂāC
SɃglʂ܂ł24bB
̗Ԃ͉̒mB

process
$1=60=3600b$ł邩C
$1b=\displaystyle\frac{1}{3600}$B
$24b=\displaystyle\frac{24}{3600}$B
Ԃ̒$x$mƂƁCӂC\\
$\displaystyle\frac{x+330}{63000}=\displaystyle\frac{24}{3600}$\\
$\displaystyle\frac{x+330}{630}=\displaystyle\frac{2}{3}$

90m

1000m̃gldԂSɒʉ߂̂1B
dԂ̒100mƂƁCdԂ͉̎kmB

process
$\displaystyle\frac{1\,{\rm km}+0.1\,{\rm km}}{1/60\,}=1.1\times 60=66$ikm/j

66km




[Level5]
ꂿlZ
200mCb15mŐiAԂƁC150mCb20mŐiBԂႤ̂ɉb܂B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic112.tex}
\end{center}
AԂ̒̐lBԂƁC15+20=35m/bŋ߂ÂB\\
$(200+150) \div 35=10$b

10b

162mCb17mŐiދ}sԂCΕ炫b13m̕ʗԂƂႤ̂10b܂B
ʗԂ͉̒młB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic113.tex}
\end{center}
}sԂ̒̐l畁ʗԂƁC17+13=30m/bŋ߂ÂB\\
$162+x=30 \times 10$

138m

́C200mAԂƁĆC140mCb21mBԂႤ̂ɁC10b܂B
AԂ͖̑bmB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic114.tex}
\end{center}
AԂ̑$v$m/bƂB
AԂ̒̐lBԂƁC$v+21$m/bŋ߂ÂB\\
$v+21=(200+140) \div 10$

b13b

120mCb14mAԂƁC150mCb16mBԂtɐiłB
2̗ԂoĂ痣܂ŉb܂B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic117.tex}
\end{center}
AԂ̒̐lBԂƁC14+16=30m/bŋ߂ÂB\\
$(120+150) \div 30=9$b

9b

2_ACBԂ̓̂1200młB
bABɍŝ12C
BAɍŝ15B
bɏoƂƁCbɂB
C͂ꂼłƂB

process
b̑
$1200m\div 12=100m/$C
̑
$1200m\div 15=80m/$B
2l̋߂Â$100+80=180m/$B
߂鎞Ԃ\\
$\displaystyle \frac{1200m}{180m/}=\displaystyle \frac{20}{3}
=6\displaystyle\frac{2}{3}$\\
$\displaystyle\frac{2}{3}=\displaystyle\frac{2}{3}\times 60b=40b$

640b

150mC100km̓dԂƁC
100mC80km̓dԂĂႤƂ
b邩B

process
$\displaystyle\frac{150+100k{\rm m}l}{(100000+80000)k{\rm m}/ԁl}\\
=\displaystyle\frac{1}{180\times 4}iԁj\\
=\displaystyle\frac{3600}{180\times 4}ibj$

5b




[Level6]
ǂzʉߗlZ
b23mŒ130mAԂCb15mŒ110mBԂɒǂĂǂz܂ŁCb܂B

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic115.tex}
\end{center}
BAƁC$(23-15)$m/bŋ߂ÂB
߂鎞Ԃ$t$ƂƁC\\
$130+110=12 \times t$

20b

100mCb17m̋}sԂCb13mő镁ʗԂ60bŒǂzĂ܂B
ʗԂ̒߂ȂB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic118.tex}
\end{center}
ʗԂ}sԂƁC$(17-13)=4$m/bŋ߂ÂB
ʗԂ̒$x$ƂƁC\\
$110+x=4 \times 60$

140m

160m̓}C200mCb20mő镁ʗԂɒǂĂ
ǂz܂ł24b܂B
}͕̑bmłB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic119.tex}
\end{center}
ʗԂ̑$v$m/bƂB
ʗԂ}ԂƁC$(v-20)$m/bŋ߂ÂB\\
$160+200=(v-20) \times 24$C$v=35$m/b

b35m

b26mC140mAԂC180mBԂɒǂĂǂz܂ł120b܂B
BԂ͕̑bmłB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic120.tex}
\end{center}
BԂ̑$v$m/bƂB
BԂAԂƁC$(26-v)$m/bŋ߂ÂB\\
$26-v=\displaystyle \frac{140+180}{80}$C$v=22$m/b

b22m

ANwZ疈60m̑ŉw܂ŕn߂3ɁA
BN75mANǂƂA
傤ǉwŒǂB
wZw܂ł͉̋mB

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/206_lZCʉߎZ/pic131.tex}
\end{center}
AB݂ƁAΑx$75-60=15$m/ŋ߂ÂB
3A$60\times 3=180$miłB
ǂ̂́ABoĂ
$\displaystyle\frac{180}{15}=12$B
߂鋗́A$75\,{\rm m}/ \times 12=900$m

900m


[Level7]


[EOF]

