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(470) About Me  (Show Source):
You can put this solution on YOUR website!
The Setup
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Equation 1: 40%2AX+%2B+58%2AY+=+646
Equation 2: X+%2B+Y+=+13
Solution:
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Solve equation 2 for one of the variables. I picked X.
X+%2B+Y+=+13 Rewrite
X+=+13+-+Y
Now plug (13 - Y) in for X in equation 1
40%2AX+%2B+58%2AY+=+646
40%2A%2813+-+Y%29+%2B+58%2AY+=+646 Multiply the 40 by (13 - Y) and rewrite
520+-+40Y+%2B+58Y+=+646 Combine like terms
520+%2B+18Y+=+646 Subtract 520 from both sides
18Y+=+126 Divide both sides by 18
Y+=+7
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
X+%2B+Y+=+13
X+%2B+7+=+13 Subtract 7 from both sides
X+=+6
Now go back to equation 1 and plug 7 in for Y, and use 6 for X.
40%2AX+%2B+58%2AY+=+646
40%2A6+%2B+58%2A7+=+646 Simplify
240+%2B+406+=+646
646+=+646