SOLUTION: A car and bus set out at the same time. The average speed of the car is 30mph slower than twice the spped of the bus. In two hours, the car is 20 miles ahead of the bus. What is th

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Question 238505: A car and bus set out at the same time. The average speed of the car is 30mph slower than twice the spped of the bus. In two hours, the car is 20 miles ahead of the bus. What is the rate of the car?
Found 2 solutions by nyc_function, josmiceli:
Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
Car's rate = 2x - 30
Car's time = 2
bus's rate = x
bus' time = 2
Your equation:
2(2x - 30) = 2x
Can you solve for x now?


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I can write 2 equations, 1 for each vehicle
d%5Bc%5D+=+r%5Bc%5D%2At%5Bc%5D
and
d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D
---------------
given:
r%5Bc%5D+=+2r%5Bb%5D+-+30 mi/hr
t%5Bc%5D+=+2 hrs
t%5Bb%5D+=+2 hrs
d%5Bc%5D+=+d%5Bb%5D+%2B+20 mi
---------------
Now I plug in the substitutions
d%5Bc%5D+=+r%5Bc%5D%2At%5Bc%5D
d%5Bb%5D+%2B+20+=+%282r%5Bb%5D+-+30%29%2A2
d%5Bb%5D+%2B+20+=+4r%5Bb%5D+-+60
(1) 4+r%5Bb%5D+-+d%5Bb%5D+=+80
and
d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D
(2) d%5Bb%5D+=+2r%5Bb%5D
Substitute (2) in (1)
(1) 4+r%5Bb%5D+-+2r%5Bb%5D+=+80
2r%5Bb%5D+=+80
r%5Bb%5D+=+40 mi/hr
and, since
r%5Bc%5D+=+2r%5Bb%5D+-+30
r%5Bc%5D+=+2%2A40+-+30
r%5Bc%5D+=+50 mi/hr
The rate of the car is 50 mi/hr
check:
d%5Bb%5D+%2B+20+=+%282r%5Bb%5D+-+30%29%2A2
d%5Bb%5D+%2B+20+=+%282%2A40+-+30%29%2A2
d%5Bb%5D+=+%2880+-+30%29%2A2+-+20
d%5Bb%5D+=+100+-+20
d%5Bb%5D+=+80 mi
and
d%5Bc%5D+=+r%5Bc%5D%2At%5Bc%5D
d%5Bc%5D+=+50%2A2
d%5Bc%5D+=+100
In 2 hours, the car is 20 mi ahead of the bus
OK