SOLUTION: It takes George 8 minutes longer to drive to work than it does to get home using the same route. If his average speed going to work is 45 mph and his average speed going home is 54

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Question 437893: It takes George 8 minutes longer to drive to work than it does to get home using the same route. If his average speed going to work is 45 mph and his average speed going home is 54 mph, how far does George live from work ?
I have absolutely no idea where to begin with this one. It seems like it would be something along the lines of: let h represent the time to get home. 45(8h)=54 but it doesn't make sense. It also seems like the solution to solve this is to have a variable on both sides. Not sure... Thank you
Found 2 solutions by ankor@dixie-net.com, htmentor:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
It takes George 8 minutes longer to drive to work than it does to get home using the same route.
If his average speed going to work is 45 mph and his average speed going home is 54 mph, how far does George live from work ?
:
since we are using mph here, change 8 min to 8/60 = 2/15 hrs
:
Find the times to and from work, and from that we can find the distance
;
Let t = time from work at 54 mph
then
(t+2%2F15) = time to work at 45 mph
:
Write a distance equation: dist = speed * time (dist both ways are equal)
54t = 45(t+2%2F15)
54t = 45t + 90%2F15
which is:
54t = 45t + 6
54t - 45t = 6
9t = 6
t = 6%2F9
t = 2%2F3 hr or 40 min
;
Find the distance using 54 mph
2%2F3 * 54 = 36 mile way from work
:
Confirm that using 45 mph, which would take 48 min; 48/60 = .8 hr
.8 * 45 = 36 mi way to work

Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
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.