SOLUTION: Thirty minutes after a father left for work on the bus, he noticed that he had left his briefcase at home. His son left hom driving at 40mph, to catch the bus that was traveling at

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Thirty minutes after a father left for work on the bus, he noticed that he had left his briefcase at home. His son left hom driving at 40mph, to catch the bus that was traveling at      Log On


   



Question 761845: Thirty minutes after a father left for work on the bus, he noticed that he had left his briefcase at home. His son left hom driving at 40mph, to catch the bus that was traveling at 24mph. How long did it take the son to catch the bus?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The father had a head start of 30 min
In terms of distance his head start was
+d%5B1%5D+=+24%2A%281%2F2%29+
+d%5B1%5D+=+12+ mi
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Start a stopwatch when the Son leaves
Let +t+ = time on stopwatch when
Son catches Father
Let +d+ = distance that Son travels
until he catches Father
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Father's equation:
+d+-+12+=+24t+
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Son's equation:
+d+=+40t+
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By substitution:
+40t+-+12++=+24t+
+16t+=+12+
+t+=+.75+ hrs
+.75%2A60+=+45+ min
It took the Son 45 min to catch the bus
check:
+d+=+40t+
+d+=+40%2A.75+
+d+=+30+
and
+d+-+12+=+24t+
+d+-+12+=+24%2A.75+
+d+=+12+%2B+18+
+d+=+30+
OK