The total time taken by a boat to cover (d+30) km in downstream and (d-60) km in upstream is (t+3) hours. The speed of stream is one fourth of the speed of boat in downstream. The same boat can cover ‘d’ distance in still water in (t-8) hours. If the speed of stream is 15 km/h, then find out the value of ‘t’.

Solution

The speed of stream is one fourth of the speed of boat in downstream.

If the speed of stream is 15 km/h.

15 = (¼) of speed of boat in downstream

speed of boat in downstream = 60 km/h

Speed of boat in still water = 60-15 = 45 km/h

 The same boat can cover ‘d’ distance in still water in (t-8) hours.

d = 45(t-8)    Eq.(i)

The total time taken by a boat to cover (d+30) km in downstream and (d-60) km in upstream is 

(t+3) hours.

[(d+30)/60] + [(d-60)/(45-15)] = (t+3)

[(d+30)/60] + [(d-60)/30] = (t+3)

Put the value of ‘d’ from Eq.(i) in the above equation.

[(45(t-8)+30)/60] + [(45(t-8)-60)/30] = (t+3)

[(45t-360+30)/60] + [(45t-360-60)/30] = (t+3)

[(45t-330)/60] + [(45t-420)/30] = (t+3)

[0.75t-5.5] + [1.5t-14] = (t+3)

2.25t-19.5 = t+3

2.25t-t = 19.5+3

1.25t = 22.5

Value of ‘t’ = 18