A train leaves San Diego at 1:00 PM. A second train leaves the same city in the same direction at 3:00 PM. The second train travels 30mph faster than the first. If the second train overtakes the first at 6:00 PM, what is the speed of each of the two trains?
Distance = Rate x Time
Train 1:
d = rt
t = 1
o PM to 6:00 PM = 5 hours
So we have d = 5r
Train 2:
d = (r + 30)t
t = 3o PM to 6:00 PM = 3 hours
So we have d = 3(r + 30)
Set both distances equal to each other since overtake means Train 2 caught up with Train 1, meaning they both traveled the same distance:
5r = 3(r + 30)
Multiply through:
3r + 90 = 5r
Run this equation through our search engine, and we get r = 45. This is Train 1's Speed.
Train 2's speed = 3(r + 30).
Plugging r = 45 into this, we get 3(45 + 30).
3(75)
225
Distance = Rate x Time
Train 1:
d = rt
t = 1
o PM to 6:00 PM = 5 hoursSo we have d = 5r
Train 2:
d = (r + 30)t
t = 3
o PM to 6:00 PM = 3 hoursSo we have d = 3(r + 30)
Set both distances equal to each other since overtake means Train 2 caught up with Train 1, meaning they both traveled the same distance:
5r = 3(r + 30)
Multiply through:
3r + 90 = 5r
Run this equation through our search engine, and we get r = 45. This is Train 1's Speed.
Train 2's speed = 3(r + 30).
Plugging r = 45 into this, we get 3(45 + 30).
3(75)
225