SOLUTION: A train leaves Miami at 2:00 pm. A second train leaves the same city traveling in the same direction at 5:00 pm. The second train travels 60 mph faster than the first. If the secon

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Question 816112: A train leaves Miami at 2:00 pm. A second train leaves the same city traveling in the same direction at 5:00 pm. The second train travels 60 mph faster than the first. If the second train overtakes the first at 8:00 pm what is the speed of each of the two trains?
Found 2 solutions by algebrahouse.com, TimothyLamb:
Answer by algebrahouse.com(1659) (Show Source):
You can put this solution on YOUR website!
Distance = rate x time

First train
rate = r
time = 6 hours {it traveled for 6 hours until it was overtaken at 8:00}
distance = 6r {distance = rate x time}

Second train
rate = r + 60 {it traveled 60 mph faster than first train}
time = 3 hours {it traveled for 3 hours before it overtook the first train}
distance = 3(r + 60) = 3r + 180 {distance = rate x time, distributive property}

6r = 3r + 180 {when the 2nd overtakes the first, their distances are equal}
3r = 180 {subtracted 3r from each side}
r = 60 {divided each side by 3}
r + 60 = 120 {substituted 60, in for r, into r + 60}

first train's rate is 60 mph
second train's rate is 120 mph

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Answer by TimothyLamb(4379) (Show Source):
You can put this solution on YOUR website!
b = a + 60
---
s = d / t
---
train 2:
s = d / t
a + 60 = D / 3
D = 3(a + 60)
---
train 1:
a = D / 6
D = 6a
---
D = 6a = 3(a + 60) = D
6a = 3a + 180
3a = 180
---
a = 60 mph
b = 120 mph
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