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Question:
A boat travels from P to Q downstream in a river and takes time 4 second. It returns to P, upstream from Q and takes time 6 second. What will be the time taken by boat to travel same distance equal to PQ in calm river?
Answer:

Let the speed of the current be x m/s

Let the speed of the boat in still water be y m/s

Now given that PQ upstream time taken = Distance / Speed

= D/ (x + y) = 4 s  --------------Eqn (1)

Similarly, QP downstream time taken = Distance / Speed

= D/ (x – y) = 6s ---------------Eqn (2)

Divide (1) by (2)

(x – y) / (x + y) = 4/6

6(x –y) = 4 (x + y)

2x = 10y which is x = 5y

Hence, Eqn (1) becomes D / (5y + y) = 4 sec

D/y = 24 sec  ---------------------Eqn (3)

Now, in a calm river or still water, same distance will be covered in time t = Distance / Speed of boat in still water = D/y which can be got from Eqn 3 as 24sec.

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