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It takes Sarah as long to paddle 10 miles downstream on a river

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It takes Sarah as long to paddle 10 miles downstream on a river [#permalink]

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New post 12 Sep 2017, 11:42
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Question Stats:

66% (01:15) correct 34% (01:22) wrong based on 89 sessions

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It takes Sarah as long to paddle 10 miles downstream on a river flowing at 3 mph as it does to paddle 12 miles down a river flowing at 4 mph. How fast does Sarah paddle in still water?

A) 4 mph

B) 3 1/2 mph

C) 3 mph

D) 2 1/2 mph

E) 2 mph

Source: 800Score
[Reveal] Spoiler: OA

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It takes Sarah as long to paddle 10 miles downstream on a river [#permalink]

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New post 12 Sep 2017, 13:47
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HKD1710 wrote:
It takes Sarah as long to paddle 10 miles downstream on a river flowing at 3 mph as it does to paddle 12 miles down a river flowing at 4 mph. How fast does Sarah paddle in still water?

A) 4 mph

B) 3 1/2 mph

C) 3 mph

D) 2 1/2 mph

E) 2 mph

Source: 800Score

It takes Sarah the same amount of time to paddle 10 miles down a river with a current of 3 mph as it does to paddle 12 miles down a river with a current of 4 mph.

Because travel times are equal, use D/r = t to find variable expressions for \(t_1\) and \(t_2\), then set \(t_1\) equal to \(t_2\) to solve for rate of Sarah's paddling.

Let x = Sarah's paddling rate in still water

First river
Distance = 10 miles
Rate = x + 3 (mph)

(Per prompt, the river current here adds 3 miles per hour to Sarah's paddling)

Time = Distance/Rate

First river TIME, \(t_1\) : \(\frac{10}{(x + 3)}\)

Second river
Distance = 12 miles
Rate = x + 4

Second river TIME, \(t_2\) : \(\frac{12}{(x + 4)}\)

Times are equal, so

\(\frac{10}{(x + 3)}\) = \(\frac{12}{(x + 4)}\)

10x + 40 = 12x + 36
4 = 2x
x = 2 mph

Answer
[Reveal] Spoiler:
E

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Re: It takes Sarah as long to paddle 10 miles downstream on a river [#permalink]

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New post 15 Sep 2017, 09:17
HKD1710 wrote:
It takes Sarah as long to paddle 10 miles downstream on a river flowing at 3 mph as it does to paddle 12 miles down a river flowing at 4 mph. How fast does Sarah paddle in still water?

A) 4 mph

B) 3 1/2 mph

C) 3 mph

D) 2 1/2 mph

E) 2 mph


We can let Sarah’s rate of paddling in still water = r. When the river is flowing at 3 mph downstream, her rate is r + 3, and when the river is flowing at 4 mph downstream, her rate is r + 4.

Recall that distance = rate x time, and thus time = distance/rate. Since it It takes Sarah as long to paddle 10 miles downstream on a river flowing at 3 mph as it does to paddle 12 miles down a river flowing at 4 mph, we set the two times equal to each other:

10/(r + 3) = 12/(r + 4)

10(r + 4) = 12(r + 3)

10r + 40 = 12r + 36

4 = 2r

2 = r

Answer: E
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It takes Sarah as long to paddle 10 miles downstream on a river [#permalink]

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New post 09 Nov 2017, 13:34
The key here is to understand that the time Sarah paddles in both cases is the same. Hence we should equate the time equation.

T = W/R

When going downstream add the speed of the water. Hence rate of Sarah for case 1 is x+3, D= 10
For case 2, Rate of Sarah is x+4 and distance is 12.

Equating both times, \(\frac{10}{(x+3)} = \frac{12}{(x+4)}\)

x = 2.

Hence, Sarah's speed in still water is 2 mph.
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It takes Sarah as long to paddle 10 miles downstream on a river   [#permalink] 09 Nov 2017, 13:34
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