Calculating speeds of two trains travelling toward one another

Question

A freight train and an express train leave towns 390 km apart, traveling toward one another.  The freight train travels 30 km per hour slower than the express train.  They pass one another 3 hours later.  What are their speeds.

Answer 1

Hi Vic.

 

We have 2 trains, freight and express.  We need to find the speed of each train, given their distance apart and the time it takes them to pass.

 

Recall

d = rt

Distance = rate times time

 

total d = 390 km

t = 3 hours

r_f = rate (speed) of freight train

r_e = rate (speed) of express train

 

We also know, from the 2nd sentence

r_f = r_e - 30

 

Putting this altogether,

 

d = r_ft + r_et

 

390 = 3r_f + 3r_e

and since r_f = r_e-30

 

390 = 3(r_e-30) + 3r_e

 

Working with this equation we have

390 = 3r_e - 90 + 3r_e

390 = 6r_e - 90

480 = 6r_e

80 = r_e

And 

r_f = r_e-30 = 80-30 = 50

 

The express train is traveling 80 km/h and the freight train is traveling 50 km/h.