Question 123084: Lois and Clark are covering separate stories and have to travel in opposite directions. Lois leaves the Daily Planet at 8:00 a.m. and travels at 35 mph. Clark leaves at 8:15 a.m. and travels at 40 mph. At what time will they be 140 mi apart?
I'm not sure how to write the equation for this problem. Thanks
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The basic equation that you use in solving this problem is the Distance equation. It states
that the Distance (D) that is traveled by a moving object is equal to the Rate of travel (R)
of the object (R) multiplied by the time the object has been traveling at that rate (T).
In equation form, this is:
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D = R*T
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Since Lois & Clark are traveling in opposite directions, the sum of the distances that each
has traveled is equal to the distance separating them.
.
Because Lois departs at 8:00, she travels for 1/4 hour (15 minutes) before Clark leaves. At
her rate of travel (35 mph) in that 1/4 hour she has gone a distance given by the equation:
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D = R*T = 35*(1/4) = 35/4 = 8.75 miles
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So at the instant Clark leaves, the distance between Lois and Clark is already 8.75 miles.
From then on the distance between them is the distance that Lois goes (35*T) plus the distance
that Clark goes in the same time T ... (40*T). Notice that T is the common time that the
two are on the road together, and T starts at 8:15.
.
So we can write the expression for the distance between them as the sum of:
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8.75 + 35*T + 40*T
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and the problem tells us that this distance is to equal 140 miles. In equation form this is:
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8.75 + 35*T + 40*T = 140
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On the left side, add the two terms that contain the factor T, and this addition reduces the
equation to:
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8.75 + 75*T = 140
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Get rid of the 8.75 on the left side by subtracting 8.75 from both sides and the result is:
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75*T = 131.25
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Solve for T by dividing both sides of this equation by 75 and the result is:
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T = 131.25/75 = 1.75
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This tells you that starting at 8:15, Lois and Clark will be 140 miles apart in an hour and
three-quarters. The three-quarters of an hour (0.75) is 45 minutes.
.
So starting at 8:15, one hour later is 9:15 and 45 minutes after that is 10:00. All times are
A.M. (in the morning) so the answer to this problem is that Lois and Clark are 140 miles
apart at 10:00 A.M.
.
Hope this helps you to understand the problem and to see a way that you can think it through
to a solution.
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