SOLUTION: Suppose a car and a truck both leave from Johannesburg. The car leaves at 09:00, and the truck leaves 45 minutes earlier. The car travels at 120 km/h and the truck travels at 90 km

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Suppose a car and a truck both leave from Johannesburg. The car leaves at 09:00, and the truck leaves 45 minutes earlier. The car travels at 120 km/h and the truck travels at 90 km      Log On

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Question 982554: Suppose a car and a truck both leave from Johannesburg. The car leaves at 09:00, and the truck leaves 45 minutes earlier. The car travels at 120 km/h and the truck travels at 90 km/h. How far away from Johannesburg will they meet?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What distance is the truck's head start?
( 45 min is 3/4 of an hour )
+d%5B1%5D+=+90%2A%283%2F4%29+
+d%5B1%5D+=+67.5+ km
----------------------
Start a stopwatch when the car leaves at 9:00
Let +t+ = time in hours on stopwatch when
car catches up with the truck
Let +d+ distance the car travels until it
catches up with the truck
-----------------------
Equation for the car:
(1) +d+=+120t+
Equation for the truck:
(2) +d+-+67.5+=+90t+
----------------------
(1) +t+=+d%2F120+
(2) +d+-+67.5+=+%28+90%2F120+%29%2Ad+
(2) +d+-+67.5+=+.75d+
(2) +.25d+=+67.5+
(2) +d+=+270+
-----------------
They meet 270 km from Johannesburg
check:
(1) +d+=+120t+
(1) +270+=+120t+
(1) +t+=+2.25+
and
(2) +d+-+67.5+=+90t+
(2) +270+-+67.5+=+90t+
(2) +202.5+=+90t+
(2) +t+=+2.25+
OK
( note that they meet at 11:15 )