An 18-year-old runner can complete a 10.0-km course with an average speed of 4.39 m/s. A 50-year-old runner can cover the same distance with an average speed of 4.27 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?
To determine how much later the younger runner should start in order to finish the course at the same time as the older runner, we can use the formula:
Time = Distance / Speed
Let's denote the time taken by the younger runner as T1 and the time taken by the older runner as T2. We need to find the time difference between T1 and T2.
For the younger runner, the time taken (T1) can be calculated as:
T1 = Distance / Speed1
For the older runner, the time taken (T2) can be calculated as:
T2 = Distance / Speed2
Since both runners will finish the course at the same time, we can set T1 equal to T2 and solve for the time difference.
T1 = T2 ⇒ Distance / Speed1 = Distance / Speed2
Cancelling out the "Distance" term on both sides of the equation:
1 / Speed1 = 1 / Speed2
To calculate the time difference in seconds, we can subtract the reciprocal of the speeds:
Time difference = 1 / Speed2 - 1 / Speed1
Plugging in the given values of Speed1 = 4.39 m/s and Speed2 = 4.27 m/s:
Time difference = 1 / 4.27 - 1 / 4.39
Calculating this expression will give us the time difference in seconds.