SOLUTION: Two vehicles are traveling a quarter of a mile. Vehicle a is going 30 mph and vehicle b is going 15 mph. Which vehicle gets there first if vehicle b is given a 20 second head start

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Question 938999: Two vehicles are traveling a quarter of a mile. Vehicle a is going 30 mph and vehicle b is going 15 mph. Which vehicle gets there first if vehicle b is given a 20 second head start? Also what are each vehicles' times?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Convert +20+ sec to minutes
+20%2F60+=+1%2F3+ min
Convert minutes to hrs
+%281%2F3%29%2A60+=+1%2F180+ hrs
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Find vehicle b's head start in miles
+d%5B1%5D+=+15%2A%281%2F180%29+
+d%5B1%5D+=+1%2F12+ mi
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Start a stopwatch when vehicle a leaves
Let +t+ = time in hrs on the stopwatch
when a get to the +1%2F4+ mi mark
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a's equation:
+1%2F4+=+30t+
+t+=+1%2F120+ hrs
+t+=+%28+1%2F120+%29%2A3600+
+t+=+30+ sec
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Start a different stopwatch when vehicle a leaves
Let +t%5B1%5D+ = time in hrs on the stopwatch
when b gets to the +1%2F4+ mi mark
b's equation:
+1%2F4+-+1%2F12+=+15t%5B1%5D+
+t%5B1%5D+=+%28+3%2F12+-+1%2F12+%29+%2F+15+
+t%5B1%5D+=+%28+1%2F6+%29%2F15+
+t%5B1%5D+=+1%2F90+ hr
+t%5B1%5D+=+%28+1%2F90+%29%2A3600+
+t%5B1%5D+=+40+ sec
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a arrives at the 1/4 mi mark first, and
beats b by +40+-+30+=+10+ sec