SOLUTION: Car A runs 30kmph less than Car B. Car A covers 250 km in the same time Car B travels 400 km. What are the rates of each car?

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Question 127073: Car A runs 30kmph less than Car B. Car A covers 250 km in the same time Car B travels 400 km. What are the rates of each car?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
car A: d%5Ba%5D+=+r%5Ba%5D%2At%5Ba%5D
car B: d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D
given: t%5Ba%5D+=+t%5Bb%5D
d%5Ba%5D+=+250km
d%5Bb%5D+=+400km
r%5Ba%5D+=+r%5Bb%5D+-+30 km/hr
putting all this together:
car A: 250+=+%28r%5Bb%5D-+30%29%2At
car B: 400+=+r%5Bb%5D%2At
solve each one for t
t+=+250+%2F+%28r%5Bb%5D+-+30%29
t+=+400+%2F+r%5Bb%5D
Set these equal to eachother
250+%2F+%28r%5Bb%5D+-+30%29+=+400+%2F+r%5Bb%5D
multiply both sides by r%5Bb%5D%2A%28r%5Bb%5D+-+30%29
250%2Ar%5Bb%5D+=+400%2A%28r%5Bb%5D+-+30%29
150%2Ar%5Bb%5D+=+12000
r%5Bb%5D+=+80
r%5Ba%5D+=+r%5Bb%5D+-+30
r%5Ba%5D+=+50
The rate of car A is 50 km/hr
The rate of car B is 80 km/hr
check answer
t+=+250+%2F+%28r%5Bb%5D+-+30%29
t+=+400+%2F+r%5Bb%5D
--------------------------
t+=+250+%2F+50
t+=+5hrs
t+=+400+%2F+80
t+=+5hrs
OK