A car leaves a town at 80 kilometers per hour. How long will it take a second car, travelling at 125 kilometers per hour, to catch the first car if it leaves 1 hour later?
the 1st car has an 80 km headstart
the difference in speeds is ... 125 kph - 80 kph = 45 kph
80 km / 45 kph = ? h
To find out how long it will take the second car to catch the first car, we can use the concept of relative motion.
First, let's assume that the time it takes for the second car to catch up with the first car is 't' hours.
Since the first car leaves 1 hour earlier, it has already been traveling for an hour when the second car starts. Therefore, the first car has already covered a distance of 80 kilometers (80 kilometers per hour * 1 hour) when the second car starts.
Now, let's consider the time it takes for the second car to catch up:
The relative speed of the second car with respect to the first car is the difference between their speeds. In this case, it is 125 kilometers per hour - 80 kilometers per hour = 45 kilometers per hour.
Since both cars are traveling in the same direction, the second car needs to cover the same distance that has been covered by the first car at this relative speed of 45 kilometers per hour. In other words, the time it takes for the second car to catch up is equal to the distance covered by the first car (80 kilometers) divided by the relative speed (45 kilometers per hour).
So, we can calculate the time 't' as:
t = 80 kilometers / 45 kilometers per hour
Simplifying this equation, we get:
t = 8/45 hours
Therefore, it will take the second car approximately 0.178 hours to catch up with the first car.
To convert this time into minutes, we can multiply the decimal value by 60:
0.178 * 60 = 10.7 minutes
So, the second car will take approximately 10.7 minutes to catch the first car.