SOLUTION: Two joggers set out at the same time from their homes 30 miles apart. They agree to meet at a point somewhere in between in two and a half hours. If the rate of one is 2 mph faster

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Question 617499: Two joggers set out at the same time from their homes 30 miles apart. They agree to meet at a point somewhere in between in two and a half hours. If the rate of one is 2 mph faster than the rate of the other, find the rate of each
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the slower jogger in mi/hr
+s+%2B+2+ = the speed of the faster jogger in mi/hr
Let +d+ = the distance the slower jogger has to
run until they meet
+30+-+d+ = the distance the faster jogger runs
-----------------
Equation for slower jogger:
(1) +d+=+s%2A2.5+
Equation for faster jogger:
(2) +30+-+d+=+%28+s+%2B+2+%29%2A2.5+
-------------------------------
Substitute (1) into (2)
(2) +30+-+2.5s+=+%28+s+%2B+2+%29%2A2.5+
(2) +30+-+2.5s+=+2.5s+%2B+5+
(2) +5s+=+30+-+5+
(2) +5s+=+25+
(2) +s+=+5+
and
+s+%2B+2+=+7+
5 mi/hr is the speed of the slower jogger
7 mi/hr is the speed of the faster jogger
check:
(2) +30+-+d+=+%28+s+%2B+2+%29%2A2.5+
(2) +30+-+d+=+7%2A2.5+
(2) +d+=+30+-+17.5+
(2) +d+=+12.5+
and
(1) +d+=+s%2A2.5+
(1) +d+=+5%2A2.5+
(1) +d+=+12.5+
OK

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two joggers set out at the same time from their homes 30 miles apart.
They agree to meet at a point somewhere in between in two and a half hours.
If the rate of one is 2 mph faster than the rate of the other, find the rate of each
:
let r = rate of the slower jogger
then
(r+2) = rate of the faster
:
Write a distance equation, dist = time * rate
2.5r + 2.5(r+2) = 30
2.5r + 2.5r + 5 = 30
5r = 30 - 5
5r = 25
r = 25/5
r = 5 mph is the slower jogger
and obviously
7 mph is the faster jogger
:
:
:
Check the total distance, to confirm our solutions
2.5(5) + 2.5(7) =
12.5 + 17.5 = 30