SOLUTION: A truck enters a highway driving 60 mph. A car enters the highway at the same place 9 minutes later and drives 66 mph in the same direction. From the time the car enters the​ hig

Algebra ->  Equations -> SOLUTION: A truck enters a highway driving 60 mph. A car enters the highway at the same place 9 minutes later and drives 66 mph in the same direction. From the time the car enters the​ hig      Log On


   

Question 1146609: A truck enters a highway driving 60 mph. A car enters the highway at the same place 9 minutes later and drives 66 mph in the same direction. From the time the car enters the​ highway, how long will it take the car to pass the​ truck?
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time for the car to pass the truck
+60%2A%28+9%2F60+%29+=+9+ miles = the truck's head start in miles
+d+ = distance in miles the car travels until it passes truck
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Start a stop watch when the car leaves
equation for the car:
(1) +d+=+66t+
equation for the truck:
(2) +d+-+9+=+60t+
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Plug (1) into (2)
(2) +66t+-+9+=+60t+
(2) +6t+=+9+
(2) +t+=+1.5+
The car takes 1.5 hrs to pass truck
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check:
(1) +d+=+66%2A1.5+
(1) +d+=+99+ mi
and
(2) +d+-+9+=+60%2A1.5+
(2) +d+-+9+=+90+
(2) +d+=+99+ mi
OK

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


60 miles per hour is 1 mile per minute.

In the 9 minutes between the times the truck and car enter the highway, the truck, at 60 mph, travels 9 miles.

The rate at which the car overtakes the truck is 66-60 = 6mph.

The time required to make up 9 miles at 6mph is 9/6 = 1.5 hours.

ANSWER: 1.5 hours