Question

A passenger train leaves the train Depot 2 hours after a freight train leaves the same depot. The freight train travels 40 mph and the passenger train at 60 mph. What time will the passenger train overtake the freight train if the freight train leaves the depot at 2:00 p.m.?

a) 3:30 p.m.
b) 4:00 p.m.
c) 4:30 p.m.
d) 5:00 p.m.

Answer 1

The passenger train will overtake the freight train 6 hours after it leaves the depot, at 8:00 p.m.

Step-by-step explanation:

To solve this problem, we can use the formula:

Distance = Speed × Time.

Let's denote the time it takes for the passenger train to overtake the freight train as t.

Since the freight train leaves at 2:00 p.m. and the passenger train leaves 2 hours later, the passenger train has been traveling for t - 2 hours when it overtakes the freight train.

Now, using the formula for distance, we can set up the following equation:

40(t) = 60(t - 2)

Simplifying the equation gives us:

40t = 60t - 120

Combining like terms:

20t = 120

Dividing both sides of the equation by 20 gives:

t = 6

Therefore, the passenger train will overtake the freight train 6 hours after it leaves the depot. Since the freight train leaves at 2:00 p.m., the passenger train will overtake it at 2:00 p.m. + 6 hours = 8:00 p.m. The correct answer is d) 5:00 p.m.