SOLUTION: You biked uphill for 3.5 hours. The return trip took 2.5 hours because you traveled 2mph faster. How far did you travel downhill?

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Question 1147421: You biked uphill for 3.5 hours. The return trip took 2.5 hours because you traveled 2mph faster. How far did you travel downhill?
Found 3 solutions by ikleyn, josmiceli, greenestamps:
Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let "d" be the unknown one-way distance, in miles.


Then the average speed biking up was  d%2F3.5  mph;  the average speed of return trip was  d%2F2.5 mph.


The difference in average rates was 2 mph


    d%2F2.5 - d%2F3.5 = 2  mph.


It is your basic equation.


To solve it, first simplify the equation


    %282d%29%2F%282%2A2.5%29 - %282d%29%2F%282%2A3.5%29 = 2,   or

    %282d%29%2F5   - %282d%29%2F7    = 2.


Next, multiply both sides by 35. You will get


    (2d)*7 - (2d)*5 = 70

    14d    - 10d    = 70

     4d             = 70

      d             = 70%2F4 = 17.5  miles.     ANSWER

Solved.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the one-way distance
Let +s+ = speed going uphill in mi/hr
----------------------------------------------
Going uphill:
(1) +d+=+s%2A3.5+
Going downhill:
(2) +d+=+%28+s+%2B+2+%29%2A2.5+
-----------------------------
+s%2A3.5+=+%28+s+%2B+2+%29%2A2.5+
+3.5s+-+2.5s+=+5+
+s+=+5+
and
(1) +d+=+5%2A3.5+
(1) +d+=+17.5+ mi
-------------------------
I traveled 17.5 mi downhill
-------------------------------
check:
(2) +d+=+%28+s+%2B+2+%29%2A2.5+
(2) +17.5+=+2.5s+%2B+5+
(2) +2.5s+=+12.5+
(2) +s+=+5+
OK

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a different way to get to the answer -- much faster than with the traditional algebraic methods shown by the other tutors.

The distances uphill and downhill are the same; since the ratio of the times is 3.5:2.5 = 7:5, the ratio of speeds is 5:7.

But 7mph is 2mph faster than 5mph; so the two speeds are 5mph and 7mph.

5mph times 3.5 hours equals 17.5 miles; or 7mph times 2.5mph equals 17.5 miles. ANSWER: 17.5 miles