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?

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(52847)   (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 mph; the average speed of return trip was mph. The difference in average rates was 2 mph - = 2 mph. It is your basic equation. To solve it, first simplify the equation - = 2, or - = 2. Next, multiply both sides by 35. You will get (2d)*7 - (2d)*5 = 70 14d - 10d = 70 4d = 70 d = = 17.5 miles. ANSWER

Solved.

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the one-way distance
Let = speed going uphill in mi/hr
----------------------------------------------
Going uphill:
(1)
Going downhill:
(2)
-----------------------------

and
(1)
(1) mi
-------------------------
I traveled 17.5 mi downhill
-------------------------------
check:
(2)
(2)
(2)
(2)
OK
Answer by greenestamps(13203)   (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
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