a boat goes 16 km upstream and 24 km downstream in 6 hrs.Also it covers 12 km upstream and 36 km downstream in the same time.Find the speed of the boat and that of the water stream.
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Answers
let the speed of boat in still water be X km/hr and the speed of water current b
e y km / hr
speed of boat in downstream =(X+y)km/hr
and that in upstream =(X+y)km/ hr
now distance =speed× time
therefore time=dustance÷speed
Time taken by the boat to travel 16km upstream =16/x-y hours and it takes 24/X+y hours to travel 24 km downstream.
by first conditio 16/x-y +24/x-y=6 equation (1)
by second condition
36/x-y + 48/X+y=13 equation (2)
replacing 1/x-y by m and 1/X+y by n we get
16m + 24n = 6. equation (3)
35m + 48n = 13 equation (4)
solving equation (3) and (4) m = 1/4, n = 1/12
replacing m,n by their original values we get
x-y = 4 (5) and X+y = 12 (6)
solving equation 5 and 6 we get X= 8 and y= 4
therefore speed of the boat in still water is 8 km/hr and speed of water current is 4 km / hr .