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

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) (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+) = time to work at 45 mph
:
Write a distance equation: dist = speed * time (dist both ways are equal)
54t = 45(t+)
54t = 45t +
which is:
54t = 45t + 6
54t - 45t = 6
9t = 6
t =
t = hr or 40 min
;
Find the distance using 54 mph
* 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) (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.
RELATED QUESTIONS
Rob drives 550 miles home in one hour less than it takes Mary to drive the same route.... (answered by Paul)
It takes Caitlyn 55 min to drive to work in the morning. She drives home using the same... (answered by ikleyn)
It takes Erica 50 min to drive to work in the morning. She drives home using the same... (answered by ikleyn)
Anayet Is drive me to work from home and realizes he left his wallet at home when he is... (answered by greenestamps)
Red Riding Hood drives 432 miles to Grandmother's house in one hour less than it takes... (answered by lwsshak3)
It's 56 miles to work, it takes 10 minutes longer to get to work than coming home, and... (answered by ankor@dixie-net.com)
It takes Erin 24 min less time to commute to work than it does George. Suppose that the... (answered by gonzo)
George left work at 2:12 it takes 45 minutes to get home what time will he get home (answered by TimothyLamb)
Johnny gets to work in 1/2 hour when he drives his car. Riding his bike (by the same... (answered by ankor@dixie-net.com)