Question

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

Explanation:

Step1: Let the length of the track be $x$ meters and the time taken be $t$ seconds.

Since time = distance/speed, for Jan, $t=\frac{x - 25}{7.5}$ (because of the 25 - m head - start), and for Mary, $t=\frac{x}{8.0}$.

Step2: Set the two time - expressions equal to each other.

$\frac{x - 25}{7.5}=\frac{x}{8.0}$
Cross - multiply: $8.0(x - 25)=7.5x$
Expand: $8.0x-200 = 7.5x$

Step3: Solve for $x$.

Subtract $7.5x$ from both sides: $8.0x-7.5x-200=0$
$0.5x=200$
Divide both sides by $0.5$: $x = 400$

Answer:

400 m