Question 92457: At 1:00 p.m., a car leaves a city and travels north at a rate of 55 mi/h. An hour later, a second car leaves the city and travels south at a rate of 60 mi/hr. At what time will the two cars be 285 miles apart?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The car going north starts at 1:00 and by 2:00 it is 55 miles to the north because it has
traveled at 55 mph for an hour.
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Since the problem asks for the time at which the cars are to be 285 miles apart and since
at 2:00 the cars are already 55 miles apart, the cars need to separate by 230 more miles because
285 - 55 = 230 miles.
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At 2:00 the separation involves 1 car going 55 mph and the other car going 60 mph in the
opposite direction. The combined separation distance will occur at the rate of 115 mph (55 mph
plus 60 mph).
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At 115 mph, how long will it take for the two cars to be 230 miles apart? Use the equation
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115*T = 230
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and solve for T by dividing both sides by 115 to get:
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T = 230/115 = 2 hours
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So in 2 hours after 2:00 the cars will be 285 miles apart ... the result of the 55 miles
of head start that the first car had plus the 230 miles covered after the second car started
out. So the time that the two cars are 285 miles apart is 2:00 + 2 hrs = 4:00. When the
clock says 4:00 the cars are 285 miles apart.
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In equation form you could get the answer by writing:
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55 + (55*T + 60*T) = 285
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where T is the time elapsed after the first car has been underway for an hour
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and this would lead to:
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55 + 115*T = 285
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Subtracting 55 from both sides:
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115*T = 230
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and by dividing both sides by 115
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T = 230/115 = 2
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The total time is the 1 hour the first car drives alone plus the 2 hours the drive together,
a total of 3 hours starting at 1:00 ... and again the answer is 4:00
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Hope this helps you to see how to analyze and solve the problem.
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