Running on a
Track Solution
Answer: ½ hour
There is no trick here; this is just simple elementary school algebra.
First, the distance formula: V*t = D
Also, we know the track is 1 mile, V1 = 3mph, V2 = 5mph
We also know that each runner completes their run in the same time, so
T1 = T2.
T1 = D1/V1
T2 = D2/V2
Thus, V2/D2 = V1/D1
Because we are on a circular track, and Jessie will run at
least one more lap (1 mile in this case) than Mark, D1 = X and D2 = 1+X
We can now set up the equation:
5/(1+x) = 3/x
X = 3/2 miles
Therefore, time = v/d = 3/(3/2) = ½ hour. Jessie will lap Mark when Mark has run 1.5
miles and Jessie has run 2.5 miles.