Question

A passenger train left the station going 63 mph. An hour earlier, a freight train left the station going 42 mph in the same direction. How many hours did it take for the passenger train to catch the freight train?

Option 1: 2 hours
Option 2: 3 hours
Option 3: 4 hours
Option 4: 5 hours

Answer 1

To find the number of hours it took for the passenger train to catch the freight train, we set up an equation using their speeds and solve for 'h'.

Step-by-step explanation:

To find out how many hours it took for the passenger train to catch the freight train, we need to determine the time needed for the passenger train to cover the same distance as the freight train.

Since the freight train left an hour earlier, the passenger train had been traveling for an hour less. Let's assume it took 'h' hours for the passenger train to catch the freight train.

Distance covered by the freight train in 'h' hours = Speed of the freight train * 'h'

Distance covered by the passenger train in 'h' - 1 hours = Speed of the passenger train * ('h' - 1)

Since both trains covered the same distance, we can set up the equation:

Speed of the freight train * 'h' = Speed of the passenger train * ('h' - 1)

Plugging in the given speeds, we get:

42 * 'h' = 63 * ('h' - 1)

Now we can solve for 'h' to find the number of hours it took for the passenger train to catch the freight train.