SOLUTION: A truck traveling at an average rate of 45 miles per hour leaves a rest stop. Fifteen minutes later a car traveling at an average rate of 60 miles per hour leaves the same rest sto

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Question 549986: A truck traveling at an average rate of 45 miles per hour leaves a rest stop. Fifteen minutes later a car traveling at an average rate of 60 miles per hour leaves the same rest stop traveling the same route. How long will it take for the car to catch up with the truck? Thanks!!!!
Found 2 solutions by josmiceli, richwmiller:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The truck has a head start of
+45%2A%281%2F4%29+=+15+ mi
Start a stopwatch when the car leaves
Let t = time on stopwatch when car catches truck
Let d = distance car travels until it catches truck
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Truck's equation:
+d+-+15+=+45t+
Car's equation:
+d+=+60t+
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By substitution:
+60t+-+15+=+45t+
+15t+=+15+
+t+=+1+
It will take the car 1 hour to catch the truck
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check:
+d+-+15+=+45%2A1+
+d+=+60+
and
+d+=+60%2A1+
+d+=+60+
OK

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
gaining speed 60 -45= 15 mph
headstart 45*0.25 =11.25 miles NOT 15
time to catch up 11.25/15=0.75 hours
time to catch up =45 minutes
distance to meeting 0.75*60=45 miles