A race car driver starts along a 50-mile race course traveling at an average speed of 90 mph. Fifteen minutes later a second driver starts along the same course at an average speed of 120 mph. Will the second car overtake the first car before the drivers reach the end of the course?
First race car driver:
time = distance / speed
time = 50 miles / 90 mph
time = 0.55556 x 60
time = 33 minutes 20 seconds
The first race car driver will took 33 minutes & 20 seconds to finish the race
Fifteen minutes later a second race car drive start
time = distance / speed
time = 50 miles / 120 mph
time = 0.41667 x 60
time = 25 minutes
The second race car driver will took 25 minutes to complete the 50 miles
Now, add 25 minutes & 15 minutes = 40 minutes
Therfore, the first race car driver will finish 6 minutes & 40 seconds before the second race car driver.
To determine whether the second car will overtake the first car before reaching the end of the course, we can calculate the time it takes for both cars to complete the race.
Let's start by calculating the time it takes for the first car to complete the race:
Distance = Speed x Time
Time = Distance / Speed
Since the distance is 50 miles and the average speed of the first car is 90 mph, we can calculate:
Time for the first car = 50 miles / 90 mph
Next, we need to calculate the time it takes for the second car to complete the race. We know that the second car starts 15 minutes (or 1/4 hour) after the first car. This means the second car has 15 minutes less time to complete the race.
Time for the second car = Time for the first car - 15 minutes
Now, we can calculate the time for the second car:
Time for the second car = (50 miles / 90 mph) - (15 minutes / 60 minutes)
Now we have the time it takes for both cars to complete the race. If the time for the second car is less than the time for the first car, then the second car will overtake the first car before reaching the end of the course.
Let's calculate the times:
Time for the first car = 50 miles / 90 mph = 0.556 hours
Time for the second car = (50 miles / 90 mph) - (15 minutes / 60 minutes) = 0.444 hours
Comparing the times, we see that the second car (0.444 hours) takes less time to complete the race than the first car (0.556 hours). Therefore, the second car will overtake the first car before reaching the end of the course.