Two cars are traveling at 40 and 50 miles per hour, respectively. If the second car starts out 5 miles behind the first car. How long will it take the second car to overtake the first car?
distance = rate x time
5 + 40x = 50x
5 = 10x
x = 1/2 hr
To determine the time it takes for the second car to overtake the first car, we need to consider the relative speed between the two cars and the initial distance between them.
Let's assume that the time it takes for the second car to overtake the first car is denoted by 't' (in hours).
We know that the first car is traveling at a speed of 40 miles per hour, and the second car is traveling at a speed of 50 miles per hour. Therefore, the relative speed between the two cars can be calculated by subtracting the speed of the first car from the speed of the second car:
Relative speed = speed of the second car - speed of the first car
= 50 mph - 40 mph
= 10 mph
Since the second car wants to catch up to the first car, it needs to cover the initial distance between them. The initial distance is given as 5 miles.
To determine the time it takes for the second car to cover this distance, we can use the formula: time = distance / speed.
Therefore, the time it takes for the second car to overtake the first car is:
t = Initial distance / Relative speed
= 5 miles / 10 mph
= 0.5 hours
Therefore, it will take the second car 0.5 hours (or 30 minutes) to overtake the first car.