SOLUTION: Van leaves traveling at 35mph, when a car traveling at 50mph leaves 45 later, when will the car catch up to the van?

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Question 492779: Van leaves traveling at 35mph, when a car traveling at 50mph leaves 45 later, when will the car catch up to the van?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The key to all of these type of problems is:
How much of a head start did the 1st
(car, boat, train) get? Then start a stopwatch
when the 2nd (car, boat, train) leaves.
Each vehicle has it's own equation.
----------------------------------
How far does the van get in 45 min?
+d%5B1%5D+=+r%2At+
+d%5B1%5D+=+35%2A%283%2F4%29+
+d%5B1%5D+=+26.25+ mi
--------------------
Star a stopwatch. They will both travel
for the same amount of time.
Equation for the car:
(1) +d%5B2%5D+=+50t+
Equation for the van:
(2) +d%5B2%5D+-+26.25+=+35t+
-------------------
There are 2 equations and 2 unknowns, so it's solvable
(2) +d%5B2%5D+=+35t+%2B+26.25+
now, I can say
+50t+=+35t+%2B+26.25+
+15t+=+26.25+
+t+=+1.75+
It will take the car 1 hr and 45 min to catch the van
------------------
check answer:
(1) +d%5B2%5D+=+50t+
(1) +d%5B2%5D+=+50%2A1.75+
(1) +d%5B2%5D+=+87.5+
and
(2) +d%5B2%5D+-+26.25+=+35t+
(2) +d%5B2%5D+=+35%2A1.75+%2B+26.25+
(2) +d%5B2%5D+=+61.25+%2B+26.25+
(2) +d%5B2%5D+=+87.5+
OK