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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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