SOLUTION: A truck driver traveled at 40 mph for the first part of a 646-mile trip, then increased his speed to 58 mph for the rest of the trip. The entire trip took 13 hours. How many hours

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Question 235375: A truck driver traveled at 40 mph for the first part of a 646-mile trip, then increased his speed to 58 mph for the rest of the trip. The entire trip took 13 hours. How many hours are traveled at 58 mph?

Answer by Stitch(43) About Me  (Show Source):
You can put this solution on YOUR website!
The Setup
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Equation 1:
Equation 2:
Solution:
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Solve equation 2 for one of the variables. I picked X.
Rewrite

Now plug (13 - Y) in for X in equation 1

Multiply the 40 by (13 - Y) and rewrite
Combine like terms
Subtract 520 from both sides
Divide both sides by 18

Now we know the the truck driver went 58mph for 7 hours.
Check Answer:
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Plug 7 into equation 2 for Y

Subtract 7 from both sides

Now go back to equation 1 and plug 7 in for Y, and use 6 for X.

Simplify