SOLUTION: Can someone help me write the equation to solve this word problem? A bus and a train start for the same destination at the same time. The highway runs along the railroad track.

Question 178582: Can someone help me write the equation to solve this word problem? A bus and a train start for the same destination at the same time. The highway runs along the railroad track. The bus averages 31mph, and the train averages 39mph. In how many hours will they be 24 miles apart?
Found 3 solutions by solver91311, josmiceli, Fombitz:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!
The difference in their speeds is 8 miles per hour. How long would it take to go 24 miles at 8 miles per hour?
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
For the bus, I can write
(1)
For the train, I can write
(2)
They are starting at the same time. Suppose I have a stopwatch
and I am high above them in a blimp or baloon.
I start the stopwatch when they both start and I can actually
measure when they are 24 mi apart, and I'll stop the watch then.
Then I will know that the elapsed time for each will be the same, or
, so I'll just call them both
given:
mi/hr
mi/hr
So far, I have:
(1)
(2)
I want the train to be mi ahead of the bus when I stop
the stopwatch, so I want

Now I can write
(1)
(2)
Substitute in (1) for in (2)

hrs
In 3 hours, they will be 24 miles apart
check:
(1)
(2)
-----------

and

OK
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Distance equals rate (speed) multiplied by time.
The distance that the bus covers is the bus' rate multiplied by time.
1.
The distance that the train covers is the train's rate multiplied by time.
2.
The difference in distance, between the train and the bus, that you're looking for is 24 miles.

Substitute using eq. 1 and eq. 2 from above and solve for t,

In 3 hours, they will be 24 miles apart.
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