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A Banana Boat travels from Sunniville to Gloomiville upstream and retu

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Bunuel
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A Banana Boat travels from Sunniville to Gloomiville upstream and retu [#permalink] New post   10 Jan 2021, 07:35
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A Banana Boat travels from Sunniville to Gloomiville upstream and returns back to Sunniville downstream. If the average speed of the total journey is 37.5 km/hr and the speed of the stream is 10 km/hr, what is the upstream speed of the Banana Boat?

A. 27.5
B. 30
C. 35
D. 40
E. 50
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B
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SherzodAzamov
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A Banana Boat travels from Sunniville to Gloomiville upstream and retu [#permalink] New post   Updated on: 15 Jan 2021, 02:15
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Bunuel wrote:
A Banana Boat travels from Sunniville to Gloomiville upstream and returns back to Sunniville downstream. If the average speed of the total journey is 37.5 km/hr and the speed of the stream is 10 km/hr, what is the upstream speed of the Banana Boat?

A. 27.5
B. 30
C. 35
D. 40
E. 50


Let's say the distance is S, speed of the boat in still water is V.
average speed is found by dividing total distance to total time:
Tu = \(\frac{S}{(V-10)}\)
Td = \(\frac{S}{(V+10)}\)

(S+S)/(Tu+Td) = 37.5
2S/(S/(V-10) + S/(V+10)) = 37.5
2/(1/(V-10) + 1/(V+10)) = 37.5
2/(2V/(V^2-100)) = 37.5
...
V^2-100 = 37.5V
V^2 - 37.5V - 100 = 0
Solving for V, we get:
V = 40
We need upstream speed, so 40 - 10=30

Answer B

Originally posted by SherzodAzamov on 11 Jan 2021, 00:19.
Last edited by SherzodAzamov on 15 Jan 2021, 02:15, edited 1 time in total.
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Pedrotri45
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Re: A Banana Boat travels from Sunniville to Gloomiville upstream and retu [#permalink] New post   15 Jan 2021, 01:44
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SherzodAzamov wrote:
Bunuel wrote:
A Banana Boat travels from Sunniville to Gloomiville upstream and returns back to Sunniville downstream. If the average speed of the total journey is 37.5 km/hr and the speed of the stream is 10 km/hr, what is the upstream speed of the Banana Boat?

A. 27.5
B. 30
C. 35
D. 40
E. 50


Let's say the distance is S, speed of the boat in still water is V.
average speed is found by dividing total distance to total time:
Tu = \(\frac{S}{(V-10)}\)
Td = \(\frac{S}{(V+10)}\)

(S+S)/(Tu+Td) = 37.5
2S/(S/(V-10) + S/(V+10)) = 37.5
2/(1/(V-10) + 1/(V+10)) = 37.5
2/(2V/(V^2-100)) = 37.5
...
V^2-100 = 37.5V
V^2 - 37.5V - 100 = 0
Solving for V, we get:
V = 40
We need upstream speed, so 40+10=50

Answer E


All good except the last line, upstream means 40-10=30
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Re: A Banana Boat travels from Sunniville to Gloomiville upstream and retu [#permalink] New post   15 Jan 2021, 02:17
Pedrotri45 wrote:
SherzodAzamov wrote:
Bunuel wrote:
A Banana Boat travels from Sunniville to Gloomiville upstream and returns back to Sunniville downstream. If the average speed of the total journey is 37.5 km/hr and the speed of the stream is 10 km/hr, what is the upstream speed of the Banana Boat?

A. 27.5
B. 30
C. 35
D. 40
E. 50


Let's say the distance is S, speed of the boat in still water is V.
average speed is found by dividing total distance to total time:
Tu = \(\frac{S}{(V-10)}\)
Td = \(\frac{S}{(V+10)}\)

(S+S)/(Tu+Td) = 37.5
2S/(S/(V-10) + S/(V+10)) = 37.5
2/(1/(V-10) + 1/(V+10)) = 37.5
2/(2V/(V^2-100)) = 37.5
...
V^2-100 = 37.5V
V^2 - 37.5V - 100 = 0
Solving for V, we get:
V = 40
We need upstream speed, so 40+10=50

Answer E


All good except the last line, upstream means 40-10=30


I guess I was in a hurry a bit. GMAT does not like hurry) Thanks buddy, for the help.
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A Banana Boat travels from Sunniville to Gloomiville upstream and retu [#permalink] New post   15 Jan 2021, 03:32
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SOLUTION:

Let speed of the boat be B kmph and one way distance be "d" km.

Total distance in the journey is 2d and the respective upstream and downstream time taken are d/(B-10) kmph & d/(B+10) kmph respectively

Given average speed of the journey is 37.5kmph.

=> 2d / [d/(B-10) + d/(B+10)] = 37.5
=> 2 / [1/(B-10) + 1/(B+10)] =37.5
=> (B-10)(B+10)/B = 37.5

Now use the options and plug in values.

If you use option B and set B-10(Upstream speed)=30=>B=40 then,
at B =40 equation (1) is (40-10)(40+10)/40 =37.5

Option (B)

Hope this helps :thumbsup:
Devmitra Sen(Math)
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Re: A Banana Boat travels from Sunniville to Gloomiville upstream and retu [#permalink] New post   17 Jan 2021, 08:49
Let speed of the boat be u kmph and one way distance be "d" km.

Total distance in the journey is 2d

We can represent the data in a table.

Given average speed of the journey is 37.5kmph.

=> 2d = 37.5 * [d/(u-10) + d/(u+10)]
=> 2 = 37.5 * [1/(u-10) + 1/(u+10)]
=> 2(u-10)(u+10)= 75* u
=> 2u^2 -75u-200=0
solving the equation, the value of u is 40, - 5/2(not acceptable)

Upstream speed is 40-10=30
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Re: A Banana Boat travels from Sunniville to Gloomiville upstream and retu [#permalink]
17 Jan 2021, 08:49
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