SOLUTION: how long will it take for a 52 mph car take to catch up to a car at 26 mph if the car at 26 mph had a 2 hour head start

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Question 746377: how long will it take for a 52 mph car take to catch up to a car at 26 mph if the car at 26 mph had a 2 hour head start
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In +2+ hrs, the slower car has a head start of
+d%5B1%5D+=+26%2A2+
+d%5B1%5D+=+52+ mi
Let +d+ = the distance the faster car goes until
it catches the slower car.
Start a stopwatch when the faster car leaves
Let +t+ = the time on the stopwatch.
Equation for faster car:
(1) +d+=+52t+
Equation for slower car:
(2) +d+-+52+=+26t+
-------------------
substitute (1) into (2)
(2) +52t+-+52+=+26t+
(2) +26t+=+52+
(2) +t+=+2+
It takes the faster car 2 hrs to catch the slower car
check:
(1) +d+=+52t+
(1) +d+=+52%2A2+
(1) +d+=+104+ mi
and
(2) +d+-+52+=+26t+
(2) +d+-+52+=+26%2A2+
(2) +d+=+52+%2B+52+
(2) +d+=+104+ mi
OK