A train moving 60mph leaves the station at noon. An hour later, a train moving 80mph leaves leading the same direction on a parallel track. In how many hours does the second train catch up with the first?

Question

A train moving 60mph leaves the station at noon. An hour later, a train moving 80mph leaves leading the same direction on a parallel track. In how many hours does the second train catch up with the first?

Answer 1

distance = rate * time ... the distances are equal

80 * t = 60 * (t + 1)

80 t = 60 t + 60 ... 20 t = 60

Answer 2

Thank you, <3

Answer 3

To find out in how many hours the second train catches up with the first, we can use the concept of relative velocity.

Let's calculate the relative velocity of the second train with respect to the first train. Since they are moving in the same direction, we can subtract their velocities.

Relative velocity = Velocity of the second train - Velocity of the first train
Relative velocity = 80 mph - 60 mph
Relative velocity = 20 mph

This means that the second train is gaining on the first train at a relative velocity of 20 mph.

Now, let's consider the time it takes for the second train to catch up with the first train. We know that the second train leaves the station one hour after the first train.

So, the first train has a one-hour head start.

Now, let's assume it takes "t" hours for the second train to catch up with the first train.

During this time, the first train will have been traveling for t + 1 hours (one-hour head start + time taken to catch up).

Since the distance traveled by both trains is the same at the point of their intersection, we can set up the equation:

Distance traveled by the first train = Distance traveled by the second train.

Using the formula Distance = Speed × Time:

60 mph × (t + 1 hour) = 80 mph × t

Simplifying the equation:

60t + 60 = 80t

Isolating the variable t:

20t = 60

t = 60 / 20

t = 3

Therefore, the second train catches up with the first train in 3 hours.