Question 406951: Bus A is 150 miles due east of Bus B. Both busses start driving due west at constant speeds at the same time. It takes Bus A 10 hours to overtake Bus B. IF they had started out at the same time, had driven at the same constant speeds, but had driven toward one another, they would have met in 2 hours. What is the speed, in miles per hour, of Bus A?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Bus A is 150 miles due east of Bus B.
Both busses start driving due west at constant speeds at the same time.
It takes Bus A 10 hours to overtake Bus B.
IF they had started out at the same time, had driven at the same constant
speeds, but had driven toward one another, they would have met in 2 hours.
What is the speed, in miles per hour, of Bus A?
:
Let a = Bus A's speed
Let b = Bus B's speed
:
Write a distance equation for each scenario
:
same direction
10a - 10b = 150
Simplify, divide by 10
a - b = 15
:
Toward each other:
2a + 2b = 150
Simplify, divide by 2
a + b = 75
:
Use elimination with these two simplified equation
a - b = 15
a + b = 75
------------ adding eliminates b, find a:
2a = 90
a = 
a = 45 mph is Bus A's speed
;
:
You can check this yourself, find b, then substitute in both equations
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