Short Note

A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

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#### Solution

Solution:

Let speed of stream = x km/h

Speed of boat in still water = 18 km/h

Speed of boat in upstream = (18 –x )km/h

Speed of boat in downstream = (18 + x ) km/h

Distance = 24 km

As per question, it takes 1 hour more to go upstream 24 km, than downstream

24 km /(18 –x ) = 24 km/(18 + x ) + 1

x^{2} + 48x – 324 = 0

x = 6 or x = – 54

But, as speed can not be negative

Hence, the speed of stream = 6 km/h

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method

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