SOLUTION: Bill Drives to work. Because of traffic conditions, he averages 30 miles per hour. He returns home averaging 40 miles per hour. The total time is four and a half hours. Write and s

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Question 997917: Bill Drives to work. Because of traffic conditions, he averages 30 miles per hour. He returns home averaging 40 miles per hour. The total time is four and a half hours. Write and solve an equation to find the time Bill spends driving to work.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
                     rate       time         distance

WORK, TRAFFIC        r%5Bw%5D       d%2Fr%5Bw%5D           d

HOME, FASTER         r%5Bh%5D       d%2Fr%5Bh%5D           d

Total                            t


The description means that these variable values are assigned:
system%28r%5Bw%5D=30%2Cr%5Bh%5D=40%2Ct=4%261%2F2%29.

The unknown variable in the whole description is d, the distance each way between work and home. The time sum equation will be what to use to solve for d.

highlight%28d%2Fr%5Bw%5D%2Bd%2Fr%5Bh%5D=t%29

d%281%2Fr%5Bw%5D%2B1%2Fr%5Bh%5D%29=t
d=t%2F%281%2Fr%5Bw%5D%2B1%2Fr%5Bh%5D%29
d=t%2F%28%28r%5Bh%5D%2Br%5Bw%5D%29%2F%28r%5Bw%5Dr%5Bh%5D%29%29
highlight%28d=%28r%5Bw%5Dr%5Bh%5Dt%29%2F%28r%5Bw%5D%2Br%5Bh%5D%29%29

You solve for d, distance each way, but not yet solved for time each way. Just use the expressions shown in the data table, substitute for d and for the given rates, and evaluate each time value.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Bill Drives to work. Because of traffic conditions, he averages 30 miles per hour. He returns home averaging 40 miles per hour. The total time is four and a half hours. Write and solve an equation to find the time Bill spends driving to work.
It's totally unnecessary to find distance, especially since you're looking for, and can determine time without doing so

Let time spent driving to work, be T

Then time spent driving home = 4%261%2F2+-+T, or 9%2F2+-+T

We then get the following distance equation: 30T+=+40%289%2F2+-+T%29

30T = 180 – 40T

30T + 40T = 180

70T = 180

T, or time spent driving to work = 180%2F70, or highlight_green%282%264%2F7%29 hours