Question
Speed of stream 'D' is 5 km/h more than speed of stream
'E'. Sum of upstream speed of a boat in 'D' and its downstream speed in 'E' is 45 km/h. Time taken by boat to cover 180 km while travelling downstream in 'D' is 5 hours. Find the difference between the upstream distance covered by boat in 'D' in 3 hours and downstream distance covered by boat in 'E' in 2 hours.Solution
Let the speed of stream 'E' be 'y' km/h and speed of boat in still water be 'v' km/h. Speed of stream 'D' = (y + 5) km/h Upstream speed of boat in 'D' = (v - y - 5) km/h Downstream speed of boat in 'E' = (v + y) km/h So, v - y - 5 + v + y = 45 Or, 2v - 5 = 45 Or, 2v = 50 Or, v = 25 Downstream speed of boat in 'D' = 25 + y + 5 = (30 + y) km/h So, 30 + y = 180/5 = 36 Or, y = 6 Upstream speed of boat in 'D' = 25 - 6 - 5 = 14 km/h Downstream speed of boat in 'E' = 25 + 6 = 31 km/h Required difference = |31 × 2 – 14 x 3|
= |62 – 42|
= 20 km
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