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

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

RELATED QUESTIONS
two buses depart from the bus staions 360 miles apart. the second bus is 10 miles per... (answered by josmiceli)

Two airplanes depart from an airport traveling opposite directions. The second airplane... (answered by checkley71)

Two airplanes depart from an airport traveling in opposite directions. The second... (answered by ukine)

Two airplanes depart from an airport traveling in opposite directions The second airplane (answered by rfer)

Two airplanes depart from an airport traveling in opposite directions. The second... (answered by ikleyn)

Two airplanes depart from an airport traveling in opposite directions.The second... (answered by Kalmetam)

Two buses are going on opposite direction. One bus goes 20 miles per hour faster than... (answered by ChrisDS)

Two airplanes depart from an airport traveling in opposite firections. The second plane... (answered by ankor@dixie-net.com)

Two buses are traveling towards each other and are doing dead-runs. One bus left the... (answered by JulietG)