An 18-year-old runner can complete a 10.0 km course with an average speed of 4.51 m/s. A 50-year-old runner can cover the same distance with an average speed of 4.31 m/s. How much later (in seconds) should the younger runner start in order to finish the course at the same time as the older runner?
The older runner requires 10,000/4.31 = 2320.2 s and the younger one requires
10,000/4.51 = 2217.3 s
The difference is 102.9 s. That is the head start required for them to finish at the same time.
To determine how much later the younger runner should start, we need to find the time it takes for each runner to complete the 10.0 km course.
Let's start by finding the time it takes for the 18-year-old runner to cover the distance. We can use the formula:
time = distance / speed
For the 18-year-old runner:
distance = 10.0 km = 10,000 m
speed = 4.51 m/s
Plugging in the values, we get:
time = 10,000 m / 4.51 m/s
Simplifying, we find that the 18-year-old runner takes approximately 2217.29 seconds to complete the course.
Now, let's find the time it takes for the 50-year-old runner to cover the same distance. Using the same formula:
For the 50-year-old runner:
distance = 10.0 km = 10,000 m
speed = 4.31 m/s
Plugging in the values, we get:
time = 10,000 m / 4.31 m/s
Simplifying, we find that the 50-year-old runner takes approximately 2321.81 seconds to complete the course.
Since we want the younger runner to finish at the same time as the older runner, the time difference between them will be zero. Therefore, the younger runner needs to start "x" seconds later.
To find "x", we can subtract the time taken by the older runner from the time taken by the younger runner:
x = 2321.81 s - 2217.29 s
Calculating, we find that the younger runner should start approximately 104.52 seconds later in order to finish the course at the same time as the older runner.