SOLUTION: A bus station runs a shuttle service to and from the airport. A shuttle that left the station traveling at 21 miles per hour is passed by a second shuttle that left 30 minutes late

Algebra ->  Linear-equations -> SOLUTION: A bus station runs a shuttle service to and from the airport. A shuttle that left the station traveling at 21 miles per hour is passed by a second shuttle that left 30 minutes late      Log On


   

Question 1092569: A bus station runs a shuttle service to and from the airport. A shuttle that left the station traveling at 21 miles per hour is passed by a second shuttle that left 30 minutes later traveling at a rate of 27 miles per hour. How far did the first shuttle travel before it was passed by the second shuttle?
If the answer is not an integer, enter it as an exact decimal.
The shuttle traveled.... miles before it was passed.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
How much of a head start in miles did the
1st shuttle get before the 2nd shuttle left?
+d%5B1%5D+=+21%2A%281%2F2%29+
+d%5B1%5D+=+10.5+ mi
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Start a stopwatch when the 2nd shuttle leaves.
Let +t+ = time in hrs on the stop watch
when the 2nd shuttle catch up with the 1st
Let +d+ = distance in miles the 2nd
shuttle travels until it catches up with the 1st
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Equation for 1st shuttle:
(1) +d+-+10.5+=+21t+
Equation for 2nd shuttle:
(2) +d+=+27t+
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Plug (2) into (1)
(1) +27t+-+10.5+=+21t+
(1) +6t+=+10.5+
(1) +t+=+1.75+ hrs
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(2) +d+=+27%2A1.75+
(2) +d+=+47.25+ mi
The 1st shuttle traveled 47.25 mi before it was passed
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check:
(1) +d+-+10.5+=+21%2A1.75+
(1) +d+-+10.5+=+36.75+
(1) +d+=+47.25+ mi
OK