<br />12. Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, andthe remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9minutes longer. Find the speed of the rickshaw and of the bus.<br />
Answers
Answer:
Speed of Rickshaw is \bold{=10\ \mathrm{km} / \mathrm{h}}=10 km/h
Speed of Bus \bold{=40\ \mathrm{km} / \mathrm{h}}=40 km/h .
Case1:
Total distance = 14km
Total time, T = 30min =\frac{1}{2} h=
2
1
h
By Rickshaw
Distance covered = 2Km
Time taken =t_{1}=t
1
Speed =\frac{\text {Distance}}{\text {Tim} e}=\frac{2}{t_{1}}=
Time
Distance
=
t
1
2
By Bus
Distance covered = 12Km
Time taken =\frac{1}{2}-t_{1}=\frac{1-2 t_{1}}{2 t_{1}}=
2
1
−t
1
=
2t
1
1−2t
1
Speed =\frac{\text {Distance}}{\text {Time}}=\frac{24 \mathrm{t}_{1}}{1-2 \mathrm{t}_{1}}=
Time
Distance
=
1−2t
1
24t
1
Case 2 :
Total distance = 14km
Total time, t_{2}=39 \min =\frac{13}{20} ht
2
=39min=
20
13
h
By Rickshaw
Distance covered = 4Km
Time taken =t_{2}=t
2
Speed =\frac{\text {Distance}}{\text {Time}}=\frac{4}{t_{2}}=
Time
Distance
=
t
2
4
In both case, Speed is equal.
Comparing Speed of rickshaw
\frac{2}{t_{1}}=\frac{4}{t_{2}} \Rightarrow t_{2}=2 t_{1}
t
1
2
=
t
2
4
⇒t
2
=2t
1
By Bus
Distance covered = 10Km
Time taken =\frac{13}{20}-t_{2}=\frac{13-20 t_{2}}{20}=
20
13
−t
2
=
20
13−20t
2
Speed =\frac{\text {Distance}}{\text {Tim} e}=\frac{200}{13-20 t_{2}}=
Time
Distance
=
13−20t
2
200
Comparing speed of bus
\frac{24 t_{1}}{1-2 t_{1}}=\frac{200}{13-20 t_{2}}
1−2t
1
24t
1
=
13−20t
2
200
3\left(13-20 t_{2}\right)=25\left(1-2 t_{1}\right)3(13−20t
2
)=25(1−2t
1
)
39-60 t_{2}=25-50 t_{1}39−60t
2
=25−50t
1
39-25=60 t 2-50 t_{1}39−25=60t2−50t
1
14=60 t_{2}-50 t 114=60t
2
−50t1
120 t_{1}-50 t_{1}=14120t
1
−50t
1
=14
70 t_{1}=1470t
1
=14
Substitute t_{2}=2 t_{1}t
2
=2t
1
t_{1}=\frac{1}{5}t
1
=
5
1
Speed of Rickshaw is =\frac{2}{t_{1}}=10 \mathrm{km} / \mathrm{h}=
t
1
2
=10km/h
Speed of Bus =\frac{24}{1-2 t_{1}}=\frac{24}{1-\frac{2}{5}}=24 \times \frac{5}{3}=40 \mathrm{km} / \mathrm{h}=
1−2t
1
24
=
1−
5
2
24
=24×
3
5
=40km/h .