SOLUTION: A car and a motorcycle both leave from the same point and travel in the same direction. (See the illustration.) The car travels at an average rate of 55 mph and the motorcycle at a

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Question 787574: A car and a motorcycle both leave from the same point and travel in the same direction. (See the illustration.) The car travels at an average rate of 55 mph and the motorcycle at an average rate of 40 mph. How long will it take before the vehicles are 5 miles apart?

Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Their rate of separation is their rate difference. 55-40=15 mph is how fast they are separating from each other.

r*t=d
15*t=5
t=1/3 hour or 20 minutes

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hours when the vehicles are
+5+ mi apart
Let +d+ = distance the car travels in +t+ hrs
----------------
Equation for car:
(1) +d+=+55t+
Equation for motorcycle:
(2) +d+-+5+=+40t+
-----------------
Substitute (1) into (2)
(2) +55t+-+5+=+40t+
(2) +15t+=+5+
(2) +t+=+1%2F3+
+%281%2F3%29%2A60+=+20+
They will be 5 mi apart in 20 minutes
check:
(1) +d+=+55%2A%281%2F3%29+
(1) +d+=+55%2F3+
and
(2) +d+-+5+=+40%2A%281%2F3%29+
(2) +d+=+15%2F3+%2B+40%2F3+
(2) +d+=+55%2F3+
OK