Question

Use the formula Time traveled = distance traveled/average velocity . A passenger train can travel 240 miles in the same amount of time it takes a freight train to travel 180 miles. If the average velocity of the freight train is 15 miles per hour slower than the average velocity of the passenger train, find the average velocity of each.

Answer 1

Alright so we have a freight train and a passenger train. Let's denote them as \(f\) and \(p\)

Answer 2

So for some constant \(t\). We know that:\[\Large t = \frac{240}{v_p}\]\[\Large t =\frac{180}{v_f}\]Which means\[\Large \frac{240}{v_p}= \frac{180}{v_f}\]

Answer 3

Now we can multiply both sides by \(v_p\) and \(v_f\) to get:\[\Large 240v_f=180v_p\]

Answer 4

We also know that, since freight is slower by 15 miles:\[\Large v_p - 15 = v_f\]

Answer 5

We have two equations and two unknowns... do you think you can solve for both \(v\)?