```Question 72383
The first bus travels from 1 p.m. to 2 p.m. at 44 mph. You can compute the distance that
this bus covers in that hour using the equation:
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D = r*t
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where D stands for distance, r is the rate or speed, and t is the amount of time.  For this
bus the rate is 44 and the elapsed time is 1 hour.  So the distance is:
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D - 44*1 = 44 miles.
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So the two buses are already 44 miles apart when the second bus departs at 2 p.m.
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Since the buses are already 44 miles apart at 2 p.m. they only need to separate by 230 more
miles (274 miles - 44 miles = 230 miles).
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Therefore, starting at 2 p.m. the distances that the two buses travel must add up to be
230 miles.  You can use the distance equation for each bus, noting that their rates
are different.  One bus has a rate of 44 mph and the other 48 mph.  So their distances
are each given by D=r*t and they must add up to be 230 miles. For the first bus you have:
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D = r*t = 44*t
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and for the second bus you have:
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D = r*t = 48*t
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Add these two together and you get:
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44t + 48t = 92t
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(Notice that t is the same for each bus because it is time that started at 2 p.m. and
both buses are underway after that time.  So the elapsed time after 2 p.m. is the same
for both buses.
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To find the time it takes to cover the 230 miles of additional separation you set the
92t equal to 230 miles.
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92t = 230
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Divide both sides by 92 to solve for t and you get:
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t = 230/92 = 2.5 hours or 2 hours and 30 minutes after 2 p.m.
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and 2 hours and 30 minutes after 2 p.m. is 4:30 p.m.  At that time they are separated
by the 230 miles plus the 44 mile head start the first bus had, so the total separation is
230 + 44 = 274 miles.
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Hope this helps you to work your way through the problem.  ```