A cruise ship travels 4 hours on a trip downstream with a 6m

A cruise ship travels 4 hours on a trip downstream with a 6-mph current. The return trip against the same current takes 5 hours. Find the speed of the boat in the water when the water is still.

Solution

let speed of boat in still water =x mph
speed of current=6mph
speed of boat in downstream=speed of boat in still water+speed of current
speed of boat in down stream=x+6 mph
speed of boat in up stream=speed of boat in still water-speed of current
speed of boat in up stream=x-6
time taken to travel down stream=4 hours
time taken to travel up stream=5 hours
distance=speed*time
distance travel downstream=speed of boat downstream/time taken to travel down stream
distance travel down stream=(x+6)*4
distance travel upstream=speed of boat upstream/time taken to travel up stream
distance travel up stream=(x-6)*5
according to the problem
distance travel downstream=distance travel up stream
(x+6)*4=(x-6)*5
4x+24=5x-30
transpose 4x on R.H.S side and -30 on L.H.S
24+30=5x-4x
54=x
speed of boat in still water=54 mph