Question

The total time taken by a boatman to row his boat upstream and downstream distance of 56 km together in 12 hours. The difference between times taken by him to row his boat another upstream and downstream distance of 42 km is 3 hours. Find the speed of boat and stream

Answer 1

Solution:

Let the speed of the boat in

still water = x km/hr

The speed of the stream = y km/hr

Speed upstream = (x-y)km/hr

Speed down stream = (x+y)km/hr

Now ,

Case1:

Total distance travelled = 56km

Time taken to cover 28km upstream = 28/(x-y) hrs

Time taken to cover 28km

down stream = 28/(x+y) hrs

But ,

total time of journey = 12 hours

28/(x-y) + 28/(x+y) = 12

Divide each term by 4,we get

=> 7/(x-y) + 7/(x+y) = 3 ---(1)

Case 2:

Time taken to cover 21 km

upstream = 21/(x-y) hr

Time taken to cover 21 km

down stream = 21/(x+y) km

In this case ,

According to the problem given,

21/(x-y) - 21/(x+y) = 3

Divide each term by 3, we get

=> 7/(x-y) - 7/(x+y) = 1 ---(2)

Let 1/(x-y) = a , 1/(x+y) = b

Now ,

equation (1) and (2) , becomes

7/a + 7/b = 3 ----(3)

7/a - 7/b = 1 ---(4)

Solving these , we get

a = 7/2 , b = 7

Therefore,

x- y = 7/2

and

x + y = 7

Solving these , we get

x = 21/4 km/hr = 5.25 km/hr

y = 7/4 km/hr

••••