Question
Speed of stream 'X' is 2 km/h more than speed of stream
'Y'. Sum of upstream speed of a boat in 'X' and its downstream speed in 'Y' is 38 km/h. Time taken by boat to cover 180 km while travelling downstream in 'X' is 5 hours. Find the difference between the upstream distance covered by boat in 'X' in 4 hours and downstream distance covered by boat in 'Y' in 2 hours.Solution
Let the speed of stream 'Y' be 'y' km/h and speed of boat in still water be 'v' km/h. Speed of stream 'X' = (y + 2) km/h Upstream speed of boat in 'X' = (v - y - 2) km/h Downstream speed of boat in 'Y' = (v + y) km/h So, v - y - 2 + v + y = 38 Or, 2v - 2 = 38 Or, 2v = 40 Or, v = 20 Downstream speed of boat in 'X' = 20 + y + 2 = (22 + y) km/h So, 22 + y = 180/5 = 36 Or, y = 14 Upstream speed of boat in 'X' = 20 - 14 - 2 = 4 km/h Downstream speed of boat in 'Y' = 20 + 14 = 34 km/h Required difference = |34 × 2 – 4 x 4|
= |68 – 16|
= 52 km
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