SOLUTION: Running at an average rate of 6 meters per second, a sprinter ran to the end of a track. The sprinter then jogged back to the starting point at an average rate of 2 meters per seco

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Running at an average rate of 6 meters per second, a sprinter ran to the end of a track. The sprinter then jogged back to the starting point at an average rate of 2 meters per seco      Log On


   

Question 771446: Running at an average rate of 6 meters per second, a sprinter ran to the end of a track. The sprinter then jogged back to the starting point at an average rate of 2 meters per second. The total time for the sprint and the jog back was 2 minutes 24 seconds. Find the length of the track.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the length of the track in meters
Let +t+ = the time spent sprinting in seconds
Convert minutes to seconds:
+2%2A60+=+120+ sec
+120+%2B+24+=+144+ sec
+144+-+t+ = time spent jogging in seconds
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Equation for sprinting:
(1) +d+=+6t+
Equation for jogging:
(2) +d+=+2%2A%28+144+-+t+%29+
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(2) +d+=+288+-+2t+
By substitution:
(2) +6t+=+288+-+2t+
(2) +8t+=+288+
(2) +t+=+36+ sec
and
(1) +d+=+6t+
(1) +d+=+6%2A36+
(1) +d+=+216+
The track is 216 meters long
check:
(2) +d+=+2%2A%28+144+-+t+%29+
(2) +216+=+2%2A%28+144+-+36+%29+
(2) +216+=+2%2A108+
(2) +216+=+216+
OK