SOLUTION: Seth and Ethan are running a race. Seth is faster than Ethan, so they decide to let Ethan get a head start. Ethan runs at 10 miles per hour and Seth runs at 15 miles per hour. How

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Question 1040900: Seth and Ethan are running a race. Seth is faster than Ethan, so they decide to let Ethan get a head start. Ethan runs at 10 miles per hour and Seth runs at 15 miles per hour. How many minutes head start did Ethan get if Seth caught up to Ethan after 60 miles?
Found 2 solutions by jorel555, josmiceli:
Answer by jorel555(1290) About Me  (Show Source):
You can put this solution on YOUR website!
60/10=6 hours running for Ethan
60/15=4 hours running for Seth
6-4=2 hours head start for Ethan ☺☺☺☺

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
let +d%5B1%5D+ = Ethan's head start in miles
-----------------------
Start a stopwatch when Seth leaves and let
+t+ = time in hours on stopwatch when
Seth catches up with Ethan
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Ethan's equation:
(1) +60+-+d%5B1%5D+=+10t+
Seth's equation:
(2) +60+=+15t+
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(2) +t+=+60%2F15+
(2) +t+=+4+
Substitute this result into (1)
(1) +60+-+d%5B1%5D+=+10%2A4+
(1) +d%5B1%5D+=+60+-+40+
(1) +d%5B1%5D+=+20+
------------------
Let +t%5B1%5D+=+Ethan%27s+head+start+in+hours%0D%0A%7B%7B%7B+d%5B1%5D+=+10%2At%5B1%5D+
+20+=+10t%5B1%5D+
+t%5B1%5D+=+2+
Ethan's head start was 120 minutes
----------------
check:
(2) +60+=+15t+
(2) +60+=+15%2A4+
(2) +60+=+60+
OK
(1) +60+-+d%5B1%5D+=+10t+
(1) +60+-+20+=+10%2A4+
(1) +40+=+40+
OK
feel free to get 2nd opinion