Two buses are traveling to a state park. One bus leaves the terminal at 4:00 p.m. and travels at 40 miles per hour. The second bus leaves the terminal at 5:00 p.m. and travels at 60 miles per hour. How much time passes until the second bus catches up with the first bus?Assessment timer and count Assessment items Two buses are traveling to a state park. One bus leaves the terminal at 4:00 p.m. and travels at 40 miles per hour. The second bus leaves the terminal at 5:00 p.m. and travels at 60 miles per hour. How much time passes until the second bus catches up with the first bus?

Answer:

Time passes until the second bus catches up with the first bus = 2 hours

Step-by-step explanation:

One bus leaves the terminal at 4:00 p.m. and travels at 40 miles per hour.

Speed of Bus 1 = 40 miles per hour

Time of leaving of Bus 1 = 4:00 p.m

The second bus leaves the terminal at 5:00 p.m. and travels at 60 miles per hour.

Speed of Bus 2= 60 miles per hour

Time of leaving of Bus 2 = 5:00 p.m

We need to find when they catch up

That is the distance traveled by them are same,

Let the time of travel for bus 1 be t, so time of travel for bus 2 is t -1

We have

                      Distance = time x Speed

                   Distance traveled buy bus 1 = Distance traveled buy bus 2

                   40 x t = 60 x (t -1 )

                   40 t = 60 t - 60

                     20t = 60

                         t = 3 hours,

So after 3 hours of starting of bus 1 they catch up,

Time passes until the second bus catches up with the first bus = t- 1 = 2 hours

Time passes until the second bus catches up with the first bus = 2 hours

The second bus takes 2 hours to catch up with the first bus after closing a gap of 40 miles at a relative speed of 20 miles per hour.

Calculating the Time for the Second Bus to Catch Up

To determine how much time passes until the second bus catches up with the first bus, we need to calculate the distance that the first bus travels before the second starts and then use the relative speeds of the buses to find out when the second bus will have covered the same distance.

The first bus travels for one hour before the second starts, covering a distance of:

Distance = speed x time = 40 miles/hour x 1 hour = 40 miles.

When the second bus starts, it closes the gap at a relative speed, which is the difference in their speeds:

Relative speed = 60 miles/hour - 40 miles/hour = 20 miles/hour.

To find out how long the second bus takes to catch up, we use the formula:

Time = Distance / Relative speed = 40 miles / 20 miles/hour = 2 hours.

So, it will take the second bus 2 hours to catch up with the first bus.

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