SOLUTION: Leo swims at 2 miles per hour in still water. After he swims down a river a quarter of a mile, returning takes three times as long as swimming downstream. Find the rate of the curr

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Question 1193084: Leo swims at 2 miles per hour in still water. After he swims down a river a quarter of a mile, returning takes three times as long as swimming downstream. Find the rate of the current.
Found 3 solutions by josgarithmetic, ankor@dixie-net.com, greenestamps:
Answer by josgarithmetic(39629) About Me  (Show Source):
You can put this solution on YOUR website!
2 mph, Leo's speed without in a current
c, speed of the current
Upstream speed 2-c
Downstream speed 2+c 
            SPEED      TIME                       DISTANCE

DOWN         2+c       +%281%2F4%29%2F%282%2Bc%29             +1%2F4

UPSTR        2-c       %281%2F4%29%2F%282-c%29               1%2F4

According to the description, %281%2F4%29%2F%282-c%29=3%281%2F4%29%2F%282%2Bc%29, and the question asks for c.

Multiply left and right side members by 4;
1%2F%282-c%29=3%2F%282%2Bc%29

2%2Bc=3%282-c%29

2%2Bc=6-3c

4c=4

highlight%28c=1%29

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Leo swims at 2 miles per hour in still water.
After he swims down a river a quarter of a mile, returning takes three times as long as swimming downstream.
Find the rate of the current.
:
let c = the rate of the current
then
(2+c) = his speed down stream
and
(2-c) = his speed upstream
:
write the dist as .25 mi
Write a time equation, time = dist/speed
.25%2F%282-c%29 = 3%28.25%2F%282%2Bc%29%29
.25%2F%282-c%29 = %28.75%2F%282%2Bc%29%29
cross multiply
.25(2+c) = .75(2-c)
.5 + .25c = 1.5 - .75c
.25c + .75c = 1.5 - .5
1c = 1
c = 1 mph is the rate of the current
:
:
Check, find the actual time each way in minutes
.25/1 = .25*60 = 15 min upstream
.25/3 = .0833*60 = 5 min downstream

Answer by greenestamps(13208) About Me  (Show Source):
You can put this solution on YOUR website!


You already have two responses from different tutors, both of which are valid, but they both make the solution more complicated than necessary.

To make the solution easier, note that the distance is not needed. The only information you need, along with the fact that he swims at 2mph, is the fact that the return trip takes three times as long.

So set the problem up like this.

let c be the speed of the current
then 2+c is his speed downstream
and 2-c is his speed upstream

Since his time returning is 3 times his time going downstream, his speed downstream is 3 times his upstream speed:

2%2Bc=3%282-c%29
2%2Bc=6-3c
4c=4
c=1

ANSWER: The speed of the current is 1mph