Im confused how I would solve this?

Question

A train leaves Santa Monica Station and travels north at a speed of 75 kilometers per hour. Two hour later, an express train leaves on a parallel track and travels north at 125 kilometers per hour. How far from the station will they meet? How would I solve this?

Answer 1

They meet when they are both the same distance from Santa Monica.

 

v₁ = speed of train 1 = 75 kph

v₂ = speed of train 2 = 125 kph

 

Let t = travel time in hours of train 1

Then t - 2 = travel time in hours of train 2 (train 2 left 2 hours after train 1)

 

The travel distances must be the same:

 

d = v₁t

d = v₂(t - 2)

 

Then

v₁t = v₂(t - 2)

Plug in the speeds and solve for t:

75t = 125(t - 2)

(125 -75)t = 250

t = 250/50 hrs = 5 hrs

 

They meet at distance

 

d = v₁t = 75*5 km = 375 km

 

You get same result if you use

 

d = v₂(t - 2) = 125*(5 - 2) km = 375 km