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A boat travels from Point A to Point B in the direction of water and

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A boat travels from Point A to Point B in the direction of water and  [#permalink]

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New post 30 Mar 2019, 05:59
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Question Stats:

36% (02:44) correct 64% (02:55) wrong based on 14 sessions

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A boat travels from Point A to Point B in the direction of water and then returns to Point A. In still water, the boat travels at a speed of 28 kilometres per hour. If the speed of the water current is 4 kilometres per hour and the time taken for the round-trip is 2 hours and 55 minutes, what is the total distance travelled by the boat in the round trip?


A. 40 kilometres
B. 71 kilometres
C. 80 kilometres
D. 82 kilometres
E. 86 kilometres
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Re: A boat travels from Point A to Point B in the direction of water and  [#permalink]

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New post 30 Mar 2019, 07:14
mangamma wrote:
A boat travels from Point A to Point B in the direction of water and then returns to Point A. In still water, the boat travels at a speed of 28 kilometres per hour. If the speed of the water current is 4 kilometres per hour and the time taken for the round-trip is 2 hours and 55 minutes, what is the total distance travelled by the boat in the round trip?


A. 40 kilometres
B. 71 kilometres
C. 80 kilometres
D. 82 kilometres
E. 86 kilometres


We are told that the boat travels 28 km/hr in still water
When moving against the water current - speed of boat is 24 km/hr
When moving for the water current - speed of boat is 32 km/hr

We can calculate the average speed using formula \(\frac{2*a*b}{(a+b)}\)

Average speed = \(\frac{2*24*32}{(24+32)} = \frac{2*24*32}{56} = \frac{6*32}{7}\)

Distance can be calulated using the formula D = S*T = \(\frac{6*32}{7} * 2\frac{55}{60} = \frac{6*32*35}{7*12} = 80\)

Therefore, the total distance travelled by the boat on the round trip is 80(Option C)
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Re: A boat travels from Point A to Point B in the direction of water and  [#permalink]

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New post 30 Mar 2019, 10:11
mangamma wrote:
A boat travels from Point A to Point B in the direction of water and then returns to Point A. In still water, the boat travels at a speed of 28 kilometres per hour. If the speed of the water current is 4 kilometres per hour and the time taken for the round-trip is 2 hours and 55 minutes, what is the total distance travelled by the boat in the round trip?


A. 40 kilometres
B. 71 kilometres
C. 80 kilometres
D. 82 kilometres
E. 86 kilometres


boat speed down stream ; 28-4 ; 24
and upstream ; 28+4; 32
avg speed of boath ; 2 * 24*32/ 56 ; 6*32/7
total time ; 120+ 55; 175 mins
so
distance travelled ; 6*32*175/ 7* 60 = 80 km
IMO C
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Re: A boat travels from Point A to Point B in the direction of water and   [#permalink] 30 Mar 2019, 10:11
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A boat travels from Point A to Point B in the direction of water and

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