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A man travels by boat 36 km down a river...

A man travels by boat 36 km down a river and back in 8 hours. If the speed of his boat in still water is 12 km/hr, find the speed of the river current.

Text Solution

Verified by Experts

The correct Answer is:
The speed of the water current is 6 km/h.
The speed of the boat in still water is 12 km/h.
Let the speed of the water current be x km/h.
Here, `xlt12`.
Then the speed of the boat downstream =(12+x)km/h and that in upstream =(12-x)km/h.
From the given condition,
`(36)/(12+x)+(36)/(12-x)=8`
`:.36(12-x+12+x)=8(12+x)(12-x)`
`:.36xx3=144-x^(2)`........ (Dividing both the sides by 8)
`:.108=144-108" ":.x^(2)=36`
`:.x=6orx=-6" ".......` (Taking square root)
But the speed cannot be negative.
`:.x=-6` is unacceptable.
`:.x=6`
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