SOLUTION: a truck drives north at 60 mph, one-and-half hour later a car drives in the the same direction at 70 mph . for how many hours must the car drive for it to be 50 miles ahead of the

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Question 811795: a truck drives north at 60 mph, one-and-half hour later a car drives in the the same direction at 70 mph . for how many hours must the car drive for it to be 50 miles ahead of the truck.
Found 2 solutions by richwmiller, josmiceli:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
In the hour and a half the truck has traveled 90 miles.
You want to get 50 ahead of the truck
That is a total of 140 miles 90+50=140
Thhe car travels ten miles faster than the truck
140/10=14 hours to get 50 miles ahead of the truck

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The truck's head start is +60%2A1.5+=+90+ mi
Let +t+ = the driving time for the car when
it is +50+ mi ahead of the truck
Let +d+ = the distance the car travels
when it meets the truck
------------------------------
Equation for truck:
(1) +d+-+90+=+60t+
Equation for car:
(2) +d+=+70t+
------------
By substitution:
(1) +70t+-+90+=+60t+
(1) +10t+=+90+
(1) +t+=+9+
------------
In 9 hrs they meet
From the place where they meet, let
the car go +d%5B2%5D+ mi, and the
truck go +d%5B2%5D+-50+
Let +t%5B2%5D+ = the time to do this
truck's equation:
(1) +d%5B2%5D+-+50+=+60t%5B2%5D+
car's equation:
(2) +d%5B2%5D+=+70t%5B2%5D+
----------------
(1) +70t%5B2%5D+-+50+=+60t%5B2%5D+
(1) +10t%5B2%5D+=+50+
(1) +t%5B2%5D+=+5+
+t+%2B+t%5B2%5D+=+9+%2B+5+
It takes 14 hrs for the car to get 50 mi ahead
of the truck