SOLUTION: A train leaves Transylvania Station at 8:00 A.M. and travels eastward at a rate of 25 miles per hour. Two hours later another train leaves the station, traveling westward at a rate

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Question 212279This question is from textbook Algebra 2 and Triginometry
: A train leaves Transylvania Station at 8:00 A.M. and travels eastward at a rate of 25 miles per hour. Two hours later another train leaves the station, traveling westward at a rate of 35 miles per hour.
c) At what time will the trains be 370 miles apart? This question is from textbook Algebra 2 and Triginometry

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
A train leaves Transylvania Station at 8:00 A.M. and travels eastward at a rate of 25 miles per hour. Two hours later another train leaves the station, traveling westward at a rate of 35 miles per hour.
c) At what time will the trains be 370 miles apart?

Step 1. Distance of train traveling eastward is 25x plus 25(2)=50 miles since it traveled for two hours before the other train started. So total distance traveled by eastward train is 25x+50 miles. And let x be the time traveled for both trains after two hours. That is, the total time traveled by the eastward train is x+2 and the westward train is x.

Step 2. Distance traveled by westward train is 35x.

Step 3. The distance traveled between the two trains is 370 miles which is equal to the sum of the distances described in Steps 1 and 2. So the equation is

25x%2B50%2B35x=370

60x%2B50=370

Step 4. Subtract 50 from both sides of equation to isolate x on one side.

60x%2B50-50=370-50

60x=320


Step 5. Divide 60 from both sides of equation.

60x%2F60=320%2F60

x=16%2F3=5%2B1%2F3 hours

Step 6. Time the trains are 370 miles apart occurs at 10 am + (5+1/3) hours or 3pm+(1/3) hour or 3:20 pm

Note: 1%2F3 hour is 1%2A60%2F3 or approximately 20 minutes.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

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