Question
A boat is traveling downstream along a river at a speed
of 60 km/h. After covering half the total distance, the speed of the river's current increases by 25%. As a result, the boat reaches its destination 15 minutes earlier than it would have under normal conditions. If the total distance to be covered by the boat is 630 km, determine the original speed of the river current.Solution
Let the speed of the stream be 'x' km/h. Original time taken to cover the journey = (630/60) = 10.5 hours So, time taken to cover the first half of the journey = 10.5 ÷ 2 = 5.25 hours Time taken to cover the second half of the journey = 5.25 hours - 15 minutes = 5 hours So, speed of the boat in second half of the journey = (315/5) = 63 km/h So, net change in speed = 63 - 60 = 3 km/h So, 1.25x - x = 3 Or, 0.25x = 3 So, 'x' = 12 Therefore, speed of the steam = 12 km/h
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