SOLUTION: Bev can drive 600 miles in the same time as it takes Sue to drive 500 miles. If Bev drives 10 mph faster than Sue, when how fast does Bev drive?

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Question 209790: Bev can drive 600 miles in the same time as it takes Sue to drive 500 miles. If Bev drives 10 mph faster than Sue, when how fast does Bev drive?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation for each one
d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D
and
d%5Bs%5D+=+r%5Bs%5D%2At%5Bs%5D
given:
d%5Bb%5D+=+600 mi
d%5Bs%5D+=+500 mi
t%5Bb%5D+=+t%5Bs%5D hr (call them both t)
r%5Bb%5D+=+r%5Bs%5D+%2B+10 mi/hr
------------------
Rewrite equations:
d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D
600+=+%28r%5Bs%5D+%2B+10%29%2At
600+=+r%5Bs%5D%2At+%2B+10t
and
d%5Bs%5D+=+r%5Bs%5D%2At%5Bs%5D
500+=+r%5Bs%5D%2At
By substitution:
600+=+500+%2B+10t
10t+=+100
t+=+10 hrs
and
600+=+r%5Bb%5D%2At
600+=+r%5Bb%5D%2A10
r%5Bb%5D+=+60 mi/hr
and
500+=+r%5Bs%5D%2At
500+=+r%5Bs%5D%2A10
r%5Bs%5D+=+50 mi/hr
Bev drives 60 mi/hr
check:
d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D
600+=+60%2A10
600+=+600
and
d%5Bs%5D+=+r%5Bs%5D%2At%5Bs%5D
500+=+50%2A10
500+=+500
OK