SOLUTION: Write an equation that can be used to solve the problem. Emily's school bus averages 28 mi/h, including stops. One day Emily forgot her backpack. Her mom left home 15 minutes (0.25

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Write an equation that can be used to solve the problem. Emily's school bus averages 28 mi/h, including stops. One day Emily forgot her backpack. Her mom left home 15 minutes (0.25      Log On

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Question 876747: Write an equation that can be used to solve the problem. Emily's school bus averages 28 mi/h, including stops. One day Emily forgot her backpack. Her mom left home 15 minutes (0.25h) after Emily and travled at an average speed of 42 mi/h. How long will it take Emily's mom to catch the bus?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
How much of a head start does the bus have?
+d%5B1%5D+=+28%2A%28+.25+%29+
+d%5B1%5D+=+7+ mi
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Start a stopwatch when her mom leaves
Let +t+ = time on stopwatch when she
catches up with the bus
Let +d+ = the distance that her mom
travels until she catches bus
----------------------
The buses equation:
(1) +d+-+7+=+28t+
Mom's equation:
(2) +d+=+42t+
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(1) +d+=+28t+%2B+7+
By substitution:
+28t+%2B+7+=+42t+
+14t+=+7+
+t+=+1%2F2+ hr
Emily's mom will catch the bus in 30 min
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check:
(1) +d+-+7+=+28%2A%28+1%2F2+%29+
(1) +d+=+21+
and
(2) +d+=+42%2A%28+1%2F2+%29+
(2) +d+=+21+
OK