Jan can run at 7.5 m/s and Mary at 8.0 m/s. On a race track Jan is given a 25m head start, and the race ends in a tie. How long is the track?
8T = 7.5T + 25.
8T-7.5T = 25
T = 50 s.
d = 8*T = 8*50 = 400 m.
To calculate the length of the track, we need to consider the time it takes for both runners to cross the finish line.
Let's assume the length of the track is "L."
Jan's speed is 7.5 m/s, and Mary's speed is 8.0 m/s.
Since Jan is given a head start of 25m, he will have covered 25m while Mary is just starting. Therefore, Jan has to travel L - 25m to cross the finish line.
Now, let's calculate the time it takes for each runner to cross the finish line:
For Jan:
Time taken by Jan = Distance / Speed = (L - 25) / 7.5
For Mary:
Time taken by Mary = Distance / Speed = L / 8.0
We are given that the race ends in a tie, meaning both runners took the same time to cross the finish line. Therefore,
(L - 25) / 7.5 = L / 8.0
To solve this equation, we can cross-multiply:
8.0 * (L - 25) = 7.5 * L
8L - 200 = 7.5L
0.5L = 200
Dividing both sides by 0.5:
L = 200 / 0.5
L = 400
Therefore, the length of the track is 400 meters.
To determine the length of the track, we need to find the time it takes for both Jan and Mary to complete the race. Since they cover the same distance (excluding Jan's head start), we can equate their respective times and distances.
Let's assume the length of the track is "x" meters. Jan runs x meters minus his head start of 25 meters, and Mary runs x meters.
The time it takes for Jan to complete the race is:
Time = Distance / Speed
Time = (x - 25) / 7.5
The time it takes for Mary to complete the race is:
Time = Distance / Speed
Time = x / 8.0
Since the race ends in a tie, Jan's time is equal to Mary's time:
(x - 25) / 7.5 = x / 8.0
To solve for x, we can cross-multiply and solve the equation:
8.0(x - 25) = 7.5x
8x - 200 = 7.5x
0.5x = 200
x = 400
Therefore, the length of the track is 400 meters.