An 18-year-old runner can complete a 10.0-km course with an average speed of 4.53 m/s. A 50-year-old runner can cover the same distance with an average speed of 3.91 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?
t1=s/v1=10000/4.53 = 2207.5 s
t2 = s/v2 = 10000/3.91 = 2557.5 s.
Δt= t2-t1= 2557.5- 2207.5= 350 s =5.83 min
To solve this problem, we need to find the time it takes for each runner to complete the 10.0-km course. We can then subtract the time of the older runner from the time of the younger runner to find the time difference.
We know that the average speed is equal to the distance divided by the time:
speed = distance / time
Let's first find the time it takes for the 18-year-old runner to complete the course:
speed = 4.53 m/s
distance = 10.0 km = 10,000 m
Rearranging the formula, we can solve for time:
time = distance / speed
Substituting the values, we can calculate the time for the 18-year-old runner:
time = 10,000 m / 4.53 m/s = 2209.27 seconds (rounded to 2 decimal places).
Now let's find the time it takes for the 50-year-old runner to complete the course:
speed = 3.91 m/s
Using the same formula, we can calculate the time for the 50-year-old runner:
time = 10,000 m / 3.91 m/s = 2556.03 seconds (rounded to 2 decimal places).
To find the time difference, we subtract the time of the older runner from the time of the younger runner:
time difference = time of 18-year-old runner - time of 50-year-old runner
time difference = 2209.27 seconds - 2556.03 seconds
time difference = -346.76 seconds (rounded to 2 decimal places).
The negative value of the time difference means that the 50-year-old runner finishes the course earlier than the 18-year-old runner. Therefore, there is no time difference for the younger runner to start later in order to finish at the same time as the older runner.