A car started out from Memphis toward Little Rock at the rate of 60km/h. A second car left from the same point 2 hours later and drove along the same route at 75km/h. How long did take the second car to overtake the first car.
The distance traveled by car A and car B is the same
distance = speed * time
car B traveled 2 hours less than car A. At time t
60t = 75(t-2)
60t = 75t - 150
15t = 150
t = 10
so, in 10 hours, car A traveled 600 km
in 8 hours, car B also traveled 600 km
The answer is, it took car B 8 hours to overtake car A.
To find out how long it took the second car to overtake the first car, we can use the concept of relative velocity.
Let's assume that the time it took the second car to overtake the first car is 't' hours.
In the 2 hours before the second car started, the first car had already traveled a distance of (60 km/h * 2 hours) = 120 kilometers.
When the second car starts, both cars are at the same point.
From that point, both cars are moving in the same direction with a relative velocity of (75 km/h - 60 km/h) = 15 km/h.
Since the second car is trying to catch up with the first car, the distance between them will decrease at a rate of 15 km/h.
Therefore, the time it takes for the second car to overtake the first car can be found using the formula:
Distance / Relative Velocity = Time
120 kilometers / 15 km/h = t
Simplifying the equation, we get:
8 hours = t
So, it took the second car 8 hours to overtake the first car.