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# A man can row at a speed of 5 km/hr in still water. If he rows a certa

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Math Expert
Joined: 02 Sep 2009
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A man can row at a speed of 5 km/hr in still water. If he rows a certa  [#permalink]

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29 Jan 2019, 04:56
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Difficulty:

55% (hard)

Question Stats:

58% (01:57) correct 42% (01:46) wrong based on 33 sessions

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A man can row at a speed of 5 km/hr in still water. If he rows a certain distance upstream and back to the starting point in a river which flows at 1.5 km/hr, what is his average speed for the double journey?

A. 3.5 km/h
B. 4.55 km/h
C. 5 km/h
D. 5.5 km/h
E. 6.5 km/h

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A man can row at a speed of 5 km/hr in still water. If he rows a certa  [#permalink]

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29 Jan 2019, 05:10
Bunuel wrote:
A man can row at a speed of 5 km/hr in still water. If he rows a certain distance upstream and back to the starting point in a river which flows at 1.5 km/hr, what is his average speed for the double journey?

A. 3.5 km/h
B. 4.55 km/h
C. 5 km/h
D. 5.5 km/h
E. 6.5 km/h

speed in upstream ; 5+1.5= 6.5kmph
down stream ; 5-1.5 = 3.5 kmph

avg speed 2 * 6.5 * 3.5 / ( 3.5 + 6.5)
IMO B 4.55
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Math Expert
Joined: 02 Aug 2009
Posts: 7334
A man can row at a speed of 5 km/hr in still water. If he rows a certa  [#permalink]

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29 Jan 2019, 05:23
Bunuel wrote:
A man can row at a speed of 5 km/hr in still water. If he rows a certain distance upstream and back to the starting point in a river which flows at 1.5 km/hr, what is his average speed for the double journey?

A. 3.5 km/h
B. 4.55 km/h
C. 5 km/h
D. 5.5 km/h
E. 6.5 km/h

Speed upstream = 5-1.5=3.5 as 1.5 km/hr is against the man's speed and speed downstream = 5+1.5km/hr=6.5 when the speed of river assists the man.
A direct formula here - $$\frac{2ab}{a+b}$$=$$\frac{2*3.5*6.5}{3.5+6.5}=\frac{7*6.5}{10}=4.55km/h$$
This is called harmonic mean and should be used when one travels half distance at speed a and other half at speed b for a return trip or equal distances.

Otherwise, the method if you do not know the formula..
upstream = 3.5 and downstream = 6.5..
Take the distance as x or say LCM of 35 and 65 = 35*13 km

total time for the trip = $$\frac{35*13}{3.5}+\frac{35*13}{6.5}=130+70=200$$ and total distance = 2*35*13=70*13=910.
average speed $$\frac{910}{200}=4.55$$
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Re: A man can row at a speed of 5 km/hr in still water. If he rows a certa  [#permalink]

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13 Feb 2019, 01:42
Bunuel wrote:
A man can row at a speed of 5 km/hr in still water. If he rows a certain distance upstream and back to the starting point in a river which flows at 1.5 km/hr, what is his average speed for the double journey?

A. 3.5 km/h
B. 4.55 km/h
C. 5 km/h
D. 5.5 km/h
E. 6.5 km/h

Let the distance traveled upstream be D
We know, Speed= Distance / Time

Time for traveling upstream = Distance/Speed = D/ 5-1.5 = D /3.5

Distance traveled upstream be D
Time for traveling upstream = Distance/Speed = D/ 5+1.5 = D /6.5

Total Time = D /3.5 + D /6.5

Average Speed = Total Distance/ Total Time = D + D / (D /3.5 + D /6.5 ) = (2D * 7 * 5 * 13) / (200 D) 4.55
Re: A man can row at a speed of 5 km/hr in still water. If he rows a certa   [#permalink] 13 Feb 2019, 01:42
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