Two trains leave a station

Question

A train leaves the station at 3:00pm and travels east at 65mph. Another train leaves the station at 4:00pm and travels in the same direction at 75mph. At what time will the second train overtake the first?

Answer 1

D = RT

First Train: D1 = (65)(t)

2nd Train: D2 = (75)(t-1)

Notes:

t = time the first train has been traveling.

2nd train has been traveling 1 hour less

than the 1st train.

We want to know the time when D1 = D2

D1 = D2

(65)t = (75)(t - 1)

65t. = 75t - 75

0 = 10t - 75

75 = 10t

7.5 = t

The 2nd train will catch up to,

then overtake the 1st train,

when t = 7.5 hours.

Recall:

t = the time the 1st train has been traveling.

And, the 1st train left the station at 3:00p

So, 7.5 later would be: 10:30 PM.

Therefore:

The 2nd train will catch up to,

then overtake the 1st train,

at 10:30 PM

Answer 2

A:

3:00 = 65mph , 4:00= 65+65 = 130mph , 5:00 = 195mph, 6:00 = 260mph 7:00= 325mph 8:00mph = 390 9:00= 455mph, 10=520mph

B:

4:00= 75mph, 5:00=150mph, 6: 00= 225mph 7:00= 300mph 8:00= 375mph 9:00= 450mph 10:00=525mph

An easier approach is to apply the trigonometric approach to be able to break down to minutes and apply modular arithmetic, however according to the level you can just find a constant rate by finding the difference from a to b. However, think about this approach to find the connection. Each cycle you are adding the previous.