SOLUTION: Note: My teacher says that the distance between Santa Fe and Topeka is not a factor in this question. At 8:00 AM a train leaves Topeka for Santa Fe and another train leaves San

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Question 761147: Note: My teacher says that the distance between Santa Fe and Topeka is not a factor in this question.
At 8:00 AM a train leaves Topeka for Santa Fe and another train leaves
Santa Fe for Topeka. The trains maintain constant speed with no stops.
The first train requires four hours to complete the trip, and the second train
requires seven hours. At what time do the trains pass each other?
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
This is what I came up with.
Distance = Rate x time.
T = time in hours
We will call the distance between the two trains X. (This will later be removed from the equation)
The rate of each train will be written as X(The total distance) divided by the time it takes for the train to cover the total distance.
Our equation wil be: T%2A%28X%2F4%29+%2B+T%2A%28X%2F7%29+=+X
Since every term contains an X we can divide both sides by X to remove it.
T%2A%281%2F4%29+%2B+T%2A%281%2F7%29+=+1
I am going to rewrite the equation.
%28T%2F4%29+%2B+%28T%2F7%29+=+1
Since the denominators are different multiply everything by 7 and by 4 to get them in the same units.

7T+%2B+4T+=+28
Combine like terms
11T+=+28
Divide both sides by 11
highlight%28T+=+2.545%29
Now you have convert the 0.545 hours to minutes.
%280.545cross%28hours%29%2F1%29%2A%2860minutes+%2F+1cross%28hours%29%29+=+32.7
Add the 2 hours and 32.7 minutes to the time of 8:00AM.
The trains should pass around 10:33AM