SOLUTION: Two buses depart from bus stations 360 miles apart. The second bus is 10 miles per hour faster than the first. After two hours they are still 120 miles apart. Find the rates of the
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Question 389456: Two buses depart from bus stations 360 miles apart. The second bus is 10 miles per hour faster than the first. After two hours they are still 120 miles apart. Find the rates of the buses. Answer by gwendolyn(128) (Show Source):
You can put this solution on YOUR website! Let S be the speed of the slow bus
Let F be the speed of the fast bus
The fast bus is 10 miles per hour faster than the slow bus.
So, F = S + 10
Two buses depart from bus stations 360 miles apart. After two hours they are still 120 miles apart. So, after two hours they have traveled a total of 360 - 120 = 240 miles. We can express the contribution to this total by each bus by using the formula distance = speed * time, where the speeds are S and F and the time is 2 hours:
2*S + 2*F = 240
Substitute the value of F from the 1st equation:
2*S + 2*(S + 10) = 240
Distribute the 2:
2*S + 2*S + 20 = 240
4*S + 20 = 240
Subtract 20 from each side to isolate the terms with the variable:
4*S + 20 - 20 = 240 - 20
4*S = 220
Divide both sides by 4:
S = 55
And substituting 55 into the first equation
F = 55 + 10
F = 65
