Speed of stream 'L' is 3 km/h more than speed of stream 'M'. Sum of upstream speed of a boat in 'L' and its downstream speed in 'M' is 39 km/h. Time taken by boat to cover 216 km while travelling downstream in 'L' is 6 hours. Find the difference between the upstream distance covered by boat in 'L' in 5 hours and downstream distance covered by boat in 'M' in 3 hours.

Solution

Let the speed of stream 'M' be 'y' km/h and speed of boat in still water be 'v' km/h. Speed of stream 'L' = (y + 3) km/h Upstream speed of boat in 'L' = (v - y - 3) km/h Downstream speed of boat in 'M' = (v + y) km/h So, v - y - 3 + v + y = 39 Or, 2v - 3 = 39 Or, 2v = 42 Or, v = 21 Downstream speed of boat in 'L' = 21 + y + 3 = (24 + y) km/h So, 24 + y = 216/6 = 36 Or, y = 12 Upstream speed of boat in 'L' = 21 - 12 - 3 = 6 km/h Downstream speed of boat in 'M' = 21 + 12 = 33 km/h Required difference = |33 × 3 – 6 x 5|
= |30 - 99|
= 69 km