Question
A motorboat moves downstream at 56 km/h. After
completing half of the route, the stream’s speed rises by 25%. Because of this, the boat reaches 20 minutes earlier than the usual time. If the total distance is 560 km, find the original speed of the stream.Solution
ATQ,
Let the speed of the stream be ‘x’ km/h. Original time for the whole journey = 560/56 = 10 hours So, time taken to cover the first half = 10 ÷ 2 = 5 hours New total time (because of early arrival) = 10 hours − 20 minutes = 9 hours 40 minutes = 9.666… hours So, time taken for the second half now = 9.666… − 5 = 4.666… hours (i.e., 4 hours 40 minutes) So, speed in the second half = 280 / 4.666… = 60 km/h Net change in speed = 60 − 56 = 4 km/h Increase due to stream = 1.25x − x = 0.25x So, 0.25x = 4 ⇒ x = 16 Therefore, the original speed of the stream = 16 km/h
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