SOLUTION: Juan drives to work. Because of traffic conditions, he averages 22 miles per hour. He returns home averaging 32 miles per hour. The total travel time is 2and1/4 hours. a. Defin

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Question 321874: Juan drives to work. Because of traffic conditions, he averages 22 miles per hour. He returns home averaging 32 miles per hour. The total travel time is 2and1/4 hours.
a. Define a variable for the time Juan takes to work. Write an expression for the time Juan takes to return home.
b. Write and solve an equation to find the time Juan spends driving to work.
Found 2 solutions by stanbon, gc2000:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Juan drives to work. Because of traffic conditions, he averages 22 miles per hour. He returns home averaging 32 miles per hour. The total travel time is 2 and 1/4 hours.
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To work DATA:
rate = 22 mph ; distance = x miles ; time = d/r = x/22 hrs
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From work DATA:
rate = 32 mph ; distance = x miles ; time = d/r = x/32 hrs
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Equation:
time + time = 2.25
x/22 + x/32 = 5/2 hr hrs
Multiply thru by 32*22 to get:
32x + 22x = 5*32*11
54x = 1760
x = 32.59 miles
Time to work = x/22 = 32.59/22 = 1.48 hrs
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Cheers,
Stan H.
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a. Define a variable for the time Juan takes to work. Write an expression for the time Juan takes to return home.
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b. Write and solve an equation to find the time Juan spends driving to work.

Answer by gc2000(22) (Show Source):
You can put this solution on YOUR website!
Correction:
Equation:
d = (r)(t)
t = d/r
let x be variable for d(istance) to work
Time to work = x/22; Time to return home = x/32
time + time = 2.25 (= 2 1/4 hrs = 9/4 hrs)
x/22 + x/32 = 9/4 hrs (NOT 5/2 = 2.5 hrs)
multiply through by 32*22:
[(32)(22)(x/22)] + [(32)(22)(x/32)] = (32)(22)(9/4)
[32x] + [22x] = (4*8)(22)(9/4) = (8)(22)(9)
54x = 1584
x = 29.333
Time to work = x/22 = 29.333/22 = 1.333hrs = 1 hr, 20 min
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ALSO, please check similar problems/solutions that set distance to work and from work as equal to each other. This alternate method may be easier to set up:
let x equal time to work (instead of distance to work as I did above)
then time to work = x
time to return = difference between total time and time to work
time to return = 2.25 - x
Set distances as equal:
distance to work = distance to return {d = (r)(t)}
(rate to work)(time to work) = (return rate)(return time)
(22)(x) = (32)(2.25 - x)
22x = 72 - 32x
add 32x to both sides of equation
54x = 72
x = 72/54 = 4/3 hrs
time to work = 1 hour 20 minutes