SOLUTION: A train leaves Washington DC at noon heading toward NY traveling 30 MPH. A train leaves New York at 2 PM heading toward DC traveling at 50 MPH. 1. If the route is 380 miles

Question 781425: A train leaves Washington DC at noon heading toward NY traveling 30 MPH. A train leaves New York at 2 PM heading toward DC traveling at 50 MPH.

1. If the route is 380 miles from NY to DC, how far apart will they be at 3PM?

2. If the route is 380 miles from NY to DC, at what time will the trains pass each other?

Thank you so much. I have been working on this problem for hours now, and I think I have just ended up confusing myself. I have come to the conclusion that the answer to #1 is 240miles. I think the answer to #2 is 6pm...but I got that by making a chart. I can't get it to come up mathematically. Using d=rt, I was able to determine that t=5, but I'm unsure what to do with this information to get the math to come out to 6pm.
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
1. If the route is 380 miles from NY to DC, how far apart will they be at 3PM?

The NY bound train traveled for 3 hours. 30*3 = 90 miles from D.C.

The D.C. bound train traveled for 1 hour. 1*50 = 50 miles from NY.

380 - (50+90) = 240 miles apart.

2. If the route is 380 miles from NY to DC, at what time will the trains pass each other?

The trains pass each other when they travel the distance between them (380 miles). Actually, the front ends of the trains reach each other when they travel that total distance, but for this problem that's considered passing.

D=RT

The trains are moving towards each other, so add their distances traveled (rt) together. The NY bound train travels for t hours, while the DC bound train travels for t-2 hours, since it left 2 hours later.

30t + 50(t-2) = 380

30t + 50t -100 = 380

80t = 480

t=480/80=6 hours. 6 hours from noon is 6PM.

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