Question 321874
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 <u>time to work</u> (instead of <u>distance to work</u> 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