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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, 12:42
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Difficulty:

  45% (medium)

Question Stats:

72% (01:04) correct 28% (01:36) wrong based on 43 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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Kudos [?]: 420 [1], given: 111

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

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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

Kudos [?]: 266 [0], given: 552

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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, 10:17
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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Kudos [?]: 837 [0], given: 5

Re: It takes Sarah as long to paddle 10 miles downstream on a river   [#permalink] 15 Sep 2017, 10:17
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