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.

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,

she has taken time to travel remaining distance i.e., (14 - 2) = 12km

By bus

By first condition,

…(i)

Now, she has taken time to travel 4 km by rickshaw,

and she has taken time to travel remaining distance i.e., (14 - 4) = 10km, by bus =

By second condition,

…(ii)

Let and then Eqs. (i) and (ii) becomes

…(iii)

and …(iv)

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

Now, put the value of v in Eq. (iii), we get

Hence, the speed of rickshaw and the bus are 10 km/h and 40 km/h, respectively.

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