SOLUTION: in a bicycle race, pete gives joey a 500 meter advantage. Also, Pete agrees to start 15 minutes after joey. If Pete bikes at 17 kilometers per hour and joey at 14 km/h, how long wi

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Question 513274: in a bicycle race, pete gives joey a 500 meter advantage. Also, Pete agrees to start 15 minutes after joey. If Pete bikes at 17 kilometers per hour and joey at 14 km/h, how long will it take pete after he starts biking to overtake joey?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Joey gets 2 head starts: one is distance and the other is time
In +15+ min, Joey bikes +.25%2A14+=+3.5+ km
His head start is +.5+%2B+3.5+=+4+ km
Start a stopwatch when Pete leaves
Pete's equation:
(1) +d+=+17t+
Joey's equation:
(2) +d+-+4+=+14t+
Note that they both travel for the same
amount of time on the stopwatch
Substitute (1) into (2)
(2) +17t+-+4+=+14t+
(2) +3t+=+4+
(2) +t+=+4%2F3+ hr
This is 1 hour plus 1/3 of an hour
Pete overtakes Joey in 1 hr and 20 min
check:
(1) +d+=+17%2A%284%2F3%29+
(1) +d+=+22.667+ km
and
(2) +d+-+4+=+14%2A%284%2F3%29+
(2) +d+=+18.667+%2B+4+
(2) +d+=+22.667+ km
Joey's time is +1.333+%2B+.25+=+1.5833+ hr
Joey's distance traveled is +22.667+-+.5+=+22.167+ km
+22.167+=+s%2A1.5833+
+s+=+22.167+%2F+1.5833+
+s+=+14.00003+ km/hr
close enough