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 ?
:
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+{{{2/15}}}) = time to work at 45 mph
:
Write a distance equation: dist = speed * time (dist both ways are equal)
54t = 45(t+{{{2/15}}})
54t = 45t + {{{90/15}}}
which is:
54t = 45t + 6
54t - 45t = 6
9t = 6
t = {{{6/9}}}
t = {{{2/3}}} hr or 40 min
;
Find the distance using 54 mph
{{{2/3}}} * 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