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A motorboat covers a given distance in 6...

A motorboat covers a given distance in `6h` moving downstream on a river. It covers the same distance in `10h` moving upstream. The time it takes to cover the same distance in still water is

A

6

B

7.5

C

10

D

15

Text Solution

Verified by Experts

The correct Answer is:
B
Let `v_w` be the velocity of water and `v_b` be the velocity of motor boat in still water . If is the distance covered , then as per question
`x=(v_(b)+v_w) xx 6 (v_b -v_w) xx10`
On solving , `v_w = (4b)/4 , :. [v_b +(4b)/4] xx 6 = 7.5 v_b`
Time taken by motor to cross the same distance in still water is
`t=(x)/v_b=(7.5v_b)/(v_b)=7.5` hours
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Knowledge Check

  • A boat covers a distance of 30 km downstream in 2 h while it takes 6 h to cover the same distance upstream.What is the speed of the boat (in km/h)?

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