jen can run at 7.5 m/s and mary at 8.0 m/s. on a race track jen is given a 25 m head start, and the race eds in a tie. how long is the track?

let x = distance run by jen.
x + 25 = distance run by mary.

time jen = d/r = x/7.5
time mary = d/r = (x+25)/8

Since they arrived at the finish line at the same time, then the times for the two are equal. Set them equal and solve for x, the distance run by jen which is the full distance of the track. Post your work if you get stuck and need further assistance. Check my thinking. Check my work carefully.

To solve this problem, let's first set up the equations based on the given information:

Distance run by Jen: x meters
Distance run by Mary: x + 25 meters

Time taken by Jen: x / 7.5 seconds
Time taken by Mary: (x + 25) / 8 seconds

Since the race ends in a tie, the time taken by Jen and Mary is the same. Therefore, we can set up the equation:

x / 7.5 = (x + 25) / 8

To solve for x, we can cross-multiply:

8x = 7.5(x + 25)

Now, let's distribute and simplify the equation:

8x = 7.5x + 187.5

Subtract 7.5x from both sides:

0.5x = 187.5

Divide both sides by 0.5:

x = 375

Therefore, the distance run by Jen, which is also the length of the track, is 375 meters.

Feel free to ask if you have any further questions or need assistance with solving the equation.