Question

A freight train leaves the station traveling due north at a speed of 40

mph. One hour later a passenger train leaves the same station
traveling due north on a parallel track at a speed of 50 mph. How
long will it take the passenger train to overtake the freight train?

Answer 1

Explanation:

t as the time (in hours) it takes for the passenger train to overtake the freight train.

The initial one-hour head start for the freight train means it has already been traveling for t + 1 hours when the passenger train starts.

Now, let's calculate the distance each train travels:

Distance = Speed × Time

For the freight train:

Distance (freight) = 40 mph × (t + 1) hours

For the passenger train:

Distance (passenger) = 50 mph × t hours

When the passenger train overtakes the freight train, they will have traveled the same distance. So, you can set up the equation:

40(t + 1) = 50t

Now, solve for t:

40t + 40 = 50t

Subtract 40t from both sides:

40 = 10t

Now, divide both sides by 10:

t = 4

So, it will take the passenger train 4 hours to overtake the freight train.