SOLUTION: Two buses leave the same city at the same time moving in opposite directions. One travels at a rate of 5 miles per hour faster than the other. After 3 hours they are 375 miles apar

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Question 268141: Two buses leave the same city at the same time moving in opposite directions. One travels at a rate of 5 miles per hour faster than the other. After 3 hours they are 375 miles apart. How far did each bus travel?

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Found 2 solutions by josmiceli, solver91311:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
speed of slower bus = s
speed of faster bus = s+%2B+5
They are moving apart at their combined speeds, which are:
s+%2B+s+%2B+5
Let d%5B1%5D = distance slower bus has gone in mi
Let d%5B2%5D = distance faster bus has gone in mi
d%5B1%5D+%2B+d%5B2%5D+=+375 mi
Since d+=+r%2At
375+=+%28s+%2B+s+%2B+5%29%2A3
375+=+6s+%2B+15
6s+=+360
s+=+60
s+%2B+5+=+65
d%5B1%5D+=+60%2A3
d%5B1%5D+=+180 mi
d%5B2%5D+=+65%2A3
d%5B2%5D+=+195 mi
The slower bus went 180 mi, the faster went 195 mi
check answer:
375+=+6s+%2B+15
375+=+6%2A60+%2B+15
375+=+360+%2B+15
375+=+375
OK

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the rate of the slower bus. Then the rate of the faster bus must be .

Since the two buses are traveling in opposite directions, the total rate is the sum of the rates of the two vehicles, namely: , or

Since distance equals rate times time:



Solve for . The distance traveled by the slower bus is . The distance traveled by the faster bus is


John