<PRE><B>Question 167614</B>
rate * time = distance
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plane 1 travels x miles per hour for 2.25 hours.
rate for plane 1 = x miles per hour.
since rate * time = distance,
distance for plane 1 = 2.25*x = d1.
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plane 2 travels (x+50) miles per hour for 1.5 hours.
rate for plane 2 = (x+50) miles per hour.
since rate * time = distance,
distance for plane 2 = 1.5*(x+50) = d2.
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since they are traveling in opposite directions, distance between them is d1 + d2.
total distance between them is given as 2325 miles.
therefore:
d1 + d2 = 2325.
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since d1 = 2.25*x
and
since d2 = 1.5*(x+50)
then
d1 + d2 = 2325 = 2.25*x + 1.5*(x+50)
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equation to solve is:
2.25*x + 1.5*(x+50) = 2325
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simplifying, this equation becomes:
2.25*x + 1.5*x + 1.5*(50) = 2325
simplifying further and combining like terms:
3.75*x + 75 = 2325
subtracting 75 from both sides of equation:
3.75*x = 2250
dividing both sides of equation by 3.75:
x = 600
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since d1 = 2.25*x, then
d1 = 2.25*(600) = 1350 miles.
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since d2 = 1.5(x+50), then
d2 = 1.5 * (650) = 975 miles.
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1350 miles + 975 miles = 2325 miles.
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plane 1 travels at 600 miles per hour.
plane 2 travels at 650 miles per hour.
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