A boat can travel 15km upstream and 18km downstream in 4 hours . Also it can go 18 km upstream and 15 km downstream in 4 hours 15 min. what is the speed of boat in still water?
Answers
speed of boat in still water is 9 km/hr
Let speed of bat in still water is x km/h and speed of current is y km/h
speed of boat in upstream direction = (x - y) km/h
speed of boat in downstream direction = (x + y) km/h
a/c to question,
15/(x - y) +18/(x + y) = 4 hrs ......(1)
18/(x - y) + 15/(x + y) = 4hrs +15 min = 4 + 1/4 = 17/4 hrs .......(2)
adding equations (1) and (2) we get,
33/(x - y) + 33/(x + y) = 4 + 17/4 = 33/4
⇒33 [1/(x - y) + 1/(x + y)] = 33/4
⇒[1/(x - y) + 1/(x + y)] = 1/4 .....(3)
now, from equation (2) and (3),
18/(x - y) + 15/(x + y) - 15/(x - y) - 15/(x + y) = 17/4 - 15/4
⇒3/(x - y) = 2/4 = 1/2
⇒x - y = 6 .......(4)
and from equation (1) we get,
1/(x + y) = 1/4 - 1/6 = 1/12
then, (x + y) = 12.......(5)
from equations (4) and (5) we get,
2x = 18 ⇒x = 9
speed of boat in still water is 9 km/h
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