2440.75 – Around the Reservoir

Tags:Problem Set 11Pre-Calculus MathAlgebra

Amy and Felicia stand at opposite each other across a circular reservoir. At a signal, they start racing around the reservoir in opposite directions. The meet for the first time after Felicia has traveled 100 yards and they meet again 60 yards before Amy has completed her first lap. What is the circumference of the circular path around the reservoir?


Let cc be the circumference of the reservoir; t1t_1 be the time of the first meeting; and t2t_2 be the time of the second meeting. Let rAr_A and rFr_F be the speeds of the two women. Then because time equals distance over rate,

t1=c2100rA=100rF,t_1 = \frac{\frac{c}{2}-100}{r_A} = \frac{100}{r_F},

t2=c+60rA=c2+60rF.t_2 = \frac{c+60}{r_A} = \frac{\frac{c}{2}+60}{r_F}.

These lead to

rFrA=100c2100=c2+60c60.\frac{r_F}{r_A} = \frac{100}{\frac{c}{2}-100} = \frac{\frac{c}{2}+60}{c-60}.

Cross multiplying gives,

(c2100)(c2+60)=100(c60).\left( \frac{c}{2}-100 \right) \left(\frac{c}{2}+60\right) = 100 (c-60).

Simplification yields the quadratic

c2=480c,c^2 = 480 c,

so that cc must be 480 yards.