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A motorboat covers the distance between ...

A motorboat covers the distance between two spots on the river banks `t_(1)=8h` and `t_(2)=12h` in down stream and upstream respectively. The time required for the boat to cover this distance in still water will be

A

9.6 h

B

11 h

C

11.8 h

D

13 h

Text Solution

Verified by Experts

Let s be the distance between that two spots. Also assume that the velocity of the motor boat in still water is v and the velocity of flow of water is u.
Then, for downstream journey,
`s//t_(1)=v+u" ….(1)"`
For upstream journey, `s//t_(2) =v-u" .....(2)"`
Adding eq. (1) to (2)
`(s)/(t_(1))+(s)/(t_(2))=2v`
or `t=(s)/(v) =(2t_(1)t_(2))/((t_(1)+t_(2)))=(2xx8xx12)/((8+12))=9.6 hr`
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