Don L. answered • 02/05/20

Fifteen years teaching and tutoring basic math skills and algebra

Hi Kenneth, this is an application of the formula: d(istance) = r(ate) * t(ime). The distance traveled by both Jim and Jessie will be the same.

Distance for Jim:

d_{Jim} = r * t

d_{Jim} = 7 * (t + 2), remember Jim runs for 2 hours more than Jessie.

Distance for Jessie:

d_{Jessie} = r * t

d_{Jessie} = 10 * t

The distance, d, for Jim and Jessie is the same. Therefore, d_{Jim} = d_{Jessie}, or 7 * (t + 2) = 10 * t.

Solve for t:

7 * (t + 2) = 10 * t

7t + 14 = 10 t

14 = 3t

t = 14/3

It will take Jessie 14/3, or 4 and 2/3 hours to catch Jim.

Check:

7 * (14/3 + 2) = 10 * 14/3

7 * 20/3 = 10 * 14/3

140/3 = 140/3

Questions?