The ratio between the speed of the boat in upstream and the speed of the stream are 6:5 respectively. The boat can cover (d+140) km distance in downstream in 28 hours. The same boat can cover (d+100) km in still water in 40 hours. Find out the time taken by the same boat to cover (d-240) km distance in upstream.

Solution

The ratio between the speed of the boat in upstream and the speed of the stream are 6:5 respectively.

Let’s assume the speed of the boat in upstream and the speed of the stream are ‘6a‘ and ‘5a‘ respectively.

Speed of boat in downstream = 6a+5a+5a = 16a

Speed of boat in still water = 16a-5a = 11a

The boat can cover (d+140) km distance in downstream in 28 hours.

(d+140)/28 = 16a

(d+140) = 448a

d = 448a-140    Eq.(i)

The same boat can cover (d+100) km in still water in 40 hours.

(d+100)/40 = 11a

(d+100) = 440a

d = 440a-100    Eq.(ii)

So Eq.(i) = Eq.(ii)

448a-140 = 440a-100

448a-440a = 140-100

8a = 40

a = 5

Put the value of ‘a’ in Eq.(i).

d = 448x5-140

= 2240-140

= 2100

Time taken by the same boat to cover (d-240) km distance in upstream = (d-240)/(6a)

Put the value of ‘d’ and ‘a’ in the above equation.

= (2100-240)/(6x5)

= 1860/30

= 62 hours