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Question

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 and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 min longer. Find the speed of the rickshaw and of the bus.

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Solution

Let the speed of the rickshaw and the bus are x and y km/h, respectively

Now, she has taken time to travel 2 km by rickshaw , t1=2xh [Speed=distancetime]
and she has taken time to travel remaining distance i.e., (14 – 2) = 12 km by bus t2=12yh
similarly, by Second condition;
t3=4xh
t4=10yh
t3+t4=12+960=12+320
4x+10y=1320

Let 1x=u 1y=v, then Eqs (i) and (ii) becomes

2u + 12v = 12

And 4u + 10v =1320

On multiplying in Eq. (iii) by 2 and then subtracting, we get

4u + 24v = 1

4u + 10v = 1320

_ _ _

14v=11320=720
2v=120v=140
Now, put the value of v in Eq (iii), we get

2u+12=(140)=12
2u=12310=5310
1x=u
1x=11010 km/h
and 1y=v1y=140
y=40 km/h
Hence, the speed of rickshaw and the bus are 10 km/h and 40 km/h, respectively.

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