SOLUTION: A train leaves a city heading west and travels at 50 miles per hour. Three hours later, a second train leaves from the same place and travels in the same direction at 65 miles per

Algebra ->  Average -> SOLUTION: A train leaves a city heading west and travels at 50 miles per hour. Three hours later, a second train leaves from the same place and travels in the same direction at 65 miles per      Log On


   



Question 128001: A train leaves a city heading west and travels at 50 miles per hour. Three hours later, a second train leaves from the same place and travels in the same direction at 65 miles per hour. How long will it take for the second train to overtake the first train?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I put a stopwatch on the 2 trains, but I wait until the moment
the 2nd train leaves. How far has the 1st train gone at that
point? 50%2A3+=+150 miles
Let t = elapsed time starting when 2nd train leaves
Let d = distance the 1st train has to travel to the point
where they meet
Then d+%2B+150 is the distance the 2nd train has to travel
to get to their meeting point
d+=+50t
d+%2B+150+=+65t
Substitute d in the 1st equation for d in the 2nd
50t+%2B+150+=+65t
15t+=+150
t+=+10 hrs
It will take the 2nd train 10 hours to overtake the 1st train
check:
d+=+50t
d+%2B+150+=+65t
-------------------
d+=+50%2A10
d+=+500 mi
-------------------
d+%2B+150+=+65t
d+=+65%2A10+-+150
d+=+500 mi
OK