Speed of stream 'P' is 3 km/h more than speed of stream 'Q'. Sum of upstream speed of a boat in 'P' and its downstream speed in 'Q' is 37 km/h. Time taken by boat to cover 168 km while travelling downstream in 'P' is 6 hours. Find the difference between the upstream distance covered by boat in 'P' in 5 hours and downstream distance covered by boat in 'Q' in 2 hours.

Solution

Let the speed of stream 'Q' be 'y' km/h and speed of boat in still water be 'v' km/h. Speed of stream 'P' = (y + 3) km/h Upstream speed of boat in 'P' = (v - y - 3) km/h Downstream speed of boat in 'Q' = (v + y) km/h So, v - y - 3 + v + y = 37 Or, 2v - 3 = 37 Or, 2v = 40 Or, v = 20 Downstream speed of boat in 'P' = 20 + y + 3 = (23 + y) km/h So, 23 + y = 168/6 = 28 Or, y = 5 Upstream speed of boat in 'P' = 20 - 5 - 3 = 12 km/h Downstream speed of boat in 'Q' = 20 + 5 = 25 km/h Required difference = 12 × 5 - 25 × 2
= 60 - 50
= 10 km