Question

A motor boat takes 6 hours to cover 100 km downstream and 30 km upstream. If the motor boat goes 75 km downstream and returns back to the starting point in 8 hours, find the speed of the boat in still water and speed of the stre

Answer 1

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Let the downstream speed = x+y=a

upstream speed = x-y=b

According to the question

100/x+y + 30/x-y = 6

75/x+y +75/x-y =8

100a+30b=6 (1)

75a+75b=8(2)

divide (1) by 2 we get

50a+15b=3 ( 3)

equating(2) and (3) we get

50a+15b = 3 (3)x5

75a+75b=8

250a+75b=15

75a+75b=8

175a=7

a=1/25 implies x+y=25 (4)

substituiting a=50 in equation(3) we get

15b=1 implies b=1/15 implies x-y=15 (5)

equating (4) and (5) we get

x+y=25

x-y=15

therefore x=20km/hr i.e. speed of motorboat in still water is 20km/hr

y=5km/hr i.e. speed of the stream is 5km/hr