Problems On Boats & Streams, General Mathematics

Question: A man rows to a place `48` km distance and back in `14` hours. He finds that he can row `4` km with the stream in the same time as `3` km against the stream. The rate of the stream is :
A
`1 km∕hr`

B
`1.8 km∕hr`

C
`3.5 km∕hr`

D
`1.5 km∕hr`

Note: Suppose he moves `4` km downstream in xj hours, Then, speed downstream `= (4/x) km∕hr,` speed downstream `= 6 km∕hr.` Rate of the stream `= 1/2 (8 - 6) km∕hr` `= 1 km∕hr.`
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Question: The current of stream runs at kmph. A motor boat goes `35` km upstream and back again to the starting point in `12` hours. The speed of the motor boat in still water is :
A
`6 km∕hr`

B
`7 km∕hr`

C
`8 km∕hr`

D
`8.5 km∕hr`

Note: Let the speed in still water be x kmph Then, speed upstream `= (x - 1) kmph, speed downstream `= (x + 1) kmph` `:. 35/(x - 1) + 35/(x + 1) = 12` `⇔ 6x^2 - 35x - 6 = 0` `:. (x - 6) (6x + 1) = 0` `or x = 6.` Hence, the speed in still water `= 6 kmph.`
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Question: A boat covers `24` km upstream and `36` km downstream in `6`hours while it covers `36` km upstream and `24` km downstream in `6 1/2` hours, The velocity of the current is :
A
`1 km∕hr`

B
`1.5 km∕hr`

C
`2 km∕hr`

D
`2.5 km∕hr`

Note: Let rate upstream = x kmph and rate downstream = y kmph Then`24/x + 36/y = 6 .....(i)` and`36/x + 24/y = 13/2 ....(ii)` Adding (i) and (ii), `60 (1/x + 1/y) = 25/2` `or 1/x + 1/y = 5/24 ... (iii)` Subtracting (i) and from (ii) `12 (1/x - 1/y) = 1/2` `or 1/x - 1/y = 1/24 .....(iv)` Adding (iii) and (iv), we get `2/x = 6/24 or x = 8.` `1/8 + 1/y = 5/24 ⇔ 1/y` `= (5/24 - 1/8) = 1/12` `⇔ y = 12. :. Speed upstream = 8 kmph, speed downstream = 12 kmph :. Rate of the current`= 1/2 (12 - 8) kmph` `= 2 kmph`
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Question: A man can row three quarters of a kilometre against the stream in `11 1/4` minutes and returns in `7 1/2` minutes. The speed of the man is still water is :
A
`2 km∕hr`

B
`3 km∕hr`

C
`4 km∕hr`

D
`5 km∕hr`

Note: Speed upstream `= (3/4 xx 4/45 xx 60) kmph` `= 4 kmph.` Speed downstream `= (3/4 xx 2/15 xx 60) kmph` `= 6 kmph.` Speed in still water `= 1/2 (6 + 4) kmph` `= 5 kmph`
1. Report

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Question: A man rows to a place `48` km distance and back in `14` hours. He finds that he can row `4` km with the stream in the same time as `3` km against the stream. The rate of the stream is :

Question: The current of stream runs at kmph. A motor boat goes `35` km upstream and back again to the starting point in `12` hours. The speed of the motor boat in still water is :

Question: A boat covers `24` km upstream and `36` km downstream in `6`hours while it covers `36` km upstream and `24` km downstream in `6 1/2` hours, The velocity of the current is :

Question: A man can row three quarters of a kilometre against the stream in `11 1/4` minutes and returns in `7 1/2` minutes. The speed of the man is still water is :