Question 437893
Let t = the time required to drive home (in hours)
Then t + 8/60 = the time required to drive to work (in hours)
The distance, d,  is the same for both drives
distance = speed x time
So for the drive to work, we have
d = 45*(t + 8/60)  [1]
And for the drive home:
d = 54*t  [2]
Since the problem asks for d, we can solve [2] for t and subsitute in [1].
Then we are left with an equation in d only:
t = d/54
d = 45(d/54 + 8/60)
Solve for d:
d = 5/6d + 45*8/60 -> 1/6d = 6 -> d = 36 miles
Therefore, the distance is 36 miles
Check:
Drive time to work = 36 mi/45mph = 0.8 hrs = 48 min
Drive time from work = 36 mi/54 mph = 2/3 hr = 40 min
The drive to work takes 8 more mins.