Question 609723
Two Sisters left at the same time to travel home. 
Susanna drove at 65 miles per hour and started 9 miles farther from home than Rachel.
 Rachel drove at 55 miles per hour.
 They reached home at the same time.
 How far was each girl from home?
;
Let d = Rachel's distance from home
then
(d+9) = Susanna's distance
:
Write a time equation; time = dist/speed
Their travel times are equal.
:
{{{d/55}}} = {{{((d+9))/65}}}
cross multiply
65d = 55(d+9)
65d = 55d + 495
65d - 55d = 495
10d = 495
d = 495/10
d = 49.5 mi, R's distance
then
49.5 + 9 = 58.5 mi, S's distance
:
:
:
See if that checks out; find the time of each; they should be equal.
49.5/55 = .9 hrs
58.5/65 = .9 hrs