800 SCORE- 5-21

[mehrasa]

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

[shankar.ashwin]

Time is constant, so distance/speed remains constant in both cases.

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

s = 2

[shankar.ashwin]

Time is constant, so distance/speed remains constant in both cases.

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

s = 2

[knight247]

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

[ntamhane]

E it is

[LalaB]

what does it mean x+3 x +4?? why??

[mehrasa]

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