The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
Answers
SOLUTION :
Given : Speed of the boat in still water= 8 km/h
Let the speed of the stream be 'x' km/h
speed of the boat in upstream = (8 - x)km/h
speed of the boat in downstream = (8 + x)km/h
Time taken by the boat to cover 15 km upstream = 15/(8- x)
[Time = distance/speed]
Time taken by the boat to cover 22 km downstream = 22/(8 + x)
A. T.Q
15/(8 - x) + 22/(8 + x) = 5
15(8 + x) + 22(8 - x) / [(8 + x)(8 - x)] = 5
[By taking LCM]
[120 + 15x + 176 - 22x] / [8² - x²] = 5
(296 - 7x) / (64 - x²) = 5
296 - 7x = 5(64 - x²)
[By cross multiplying]
296 - 7x = 320 - 5x²
5x² - 320 - 7x + 296 = 0
5x² - 7x - 24 = 0
5x² - 15x + 8x - 24 = 0
[By middle term splitting]
5x(x - 3) + 8(x - 3) = 0
(5x + 8) (x - 3) = 0
(5x + 8) = 0 or (x - 3) = 0
5x = - 8 or x = 3
x = - 8/5 or x = 3
Since, speed of the stream can't be negative, so x ≠ - 8/5
Therefore, x = 3
Hence the speed of the stream is 3 km/h
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