SOLUTION: A train leaves a station and travels north at 75km/h. Two hours later, a second train leaves on a parallel track traveling north at 125km/h. How far from the station will the secon

Question 1145488: A train leaves a station and travels north at 75km/h. Two hours later, a second train leaves on a parallel track traveling north at 125km/h. How far from the station will the second train overtake the first train?

Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
r*t=d
r = rate
t = time
d = distance

for the first train, the formula becomes 75 * t = d
for the second train, the formula becomes 125 * (t-2) = d

the second train will overtake the first train after they both have traveled the same distance.

since both equal to d, then both equal to each other and you get:
75 * t = 125 * (t-2)
simplify to get 75 * t = 125 * t - 250
subtract 75 * t from both sides and add 250 to both sides to get:
250 = 125 * t - 75 * t
combine like terms to get 250 = 50 * t
solve for t to get t= 5

the second train will overtake the first train after they have both traveled for 5 hours.

75 * 5 = 375
125 * 3 = 375

at exactly 5 hours, both trains will be neck and neck.
after 5 hours, the second train will have traveled a greater distance than the first train.

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

A train leaves a station and travels north at 75km/h. Two hours later, a second train leaves on a parallel track traveling north at 125km/h. How far from the station will the second train overtake the first train?

Let distance be D
When the 2nd train pulls up alongside the 1st train, and their "noses" are perpendicular to each other, both trains will have traveled the same distance
Therefore, we get the following TIME equation:
5D = 3D + 2(375) -------- Multiplying by LCD, 375
5D - 3D = 2(375)
2D = 2(375)
D, or
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