SOLUTION: Two straight roads intersect at right angles. At 10:00 a.m. a car passes through the intersection headed due east at 30 miles per hour. At 11:00 a.m. a truck heading due north at

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Question 315464: Two straight roads intersect at right angles. At 10:00 a.m. a car passes through the
intersection headed due east at 30 miles per hour. At 11:00 a.m. a truck heading due
north at 40 miles per hour passes through the intersection. Assume that the two vehicles
maintain the given speeds and directions. At what rate are they separating at 1:00 p.m.?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Two straight roads intersect at right angles.
At 10:00 a.m. a car passes through the intersection headed due east at 30 miles per hour.
At 11:00 a.m. a truck heading due north at 40 miles per hour passes through the intersection.
Assume that the two vehicles maintain the given speeds and directions.
At what rate are they separating at 1:00 p.m.?
:
From the given information:
At 1 pm:
truck travel time = 2 hrs
Car travel time = 3 hrs
:
Find the dist between the vehicles using pythag: c^2 = a^2 + b^2
Distance at 2 PM
a = 4(30) = 120 mi
b = 3(40) = 120 mi
c = sqrt%28120%5E2+%2B+120%5E2%29
c = 169.7 mi apart at 2 PM
:
Find the distance at 12 noon
a = 2(30) = 60 mi
b = 1(40) = 40 mi
c = sqrt%2860%5E2+%2B+40%5E2%29
c = 72.1 mi apart at 12 noon
:
12 noon to 2 pm separation distance: 169.7 - 72.1 = 97.6 mi
Average rate of separation 97.6/2 = 48.8 mph separation rate at 1 pm