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by mehrasa » Sat Sep 24, 2011 11:58 pm
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
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by shankar.ashwin » Sun Sep 25, 2011 12:09 am
Time is constant, so distance/speed remains constant in both cases.

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

s = 2
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by shankar.ashwin » Sun Sep 25, 2011 12:09 am
Time is constant, so distance/speed remains constant in both cases.

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

s = 2
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by knight247 » Sun Sep 25, 2011 12:27 am
Lets Sarah's speed be x under normal circumstances.

For River A
Distance=10
Speed=x+3
Time=10/(x+3)


For River B
Distance=12
Speed=x+4
Time=12/(x+4)

Both times are given to be equal so
10/(x+3)=12/(x+4)
x=2

Her speed is 2mph in still water. Hence E
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by ntamhane » Sun Sep 25, 2011 3:19 am
E it is
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by LalaB » Sun Sep 25, 2011 5:11 am
what does it mean x+3 x +4?? why??
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by mehrasa » Sun Sep 25, 2011 5:39 am
LalaB wrote:what does it mean x+3 x +4?? why??
sarah's velocity= still water speed + river flow (boat speed, if any)
Sarah's velocity in downstream = X+3
and in the upstream route ==> Sarah's velocity is X+4
since the time of upstream=time of downstream ==> D/X+3=D/X+4 on the other hand, distance for downstream and upstream is 10 and 12 ==> 10/x+3 = 12/x+4 ==> x=2 which is still water velocity
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