Solve the problem by setting up and solving an appropriate algebraic equation.

Question

Juan starts walking at 4 miles per hour. An hour and a half later, Cathy starts jogging along the same route at 5 miles per hour. How long will it take Cathy to catch up with Juan?

Answer 1

In order for Cathy to catch up with Juan, they both have to cover the same distance (d)

distance (d) = speed (s) * time (t)

Juan's time is 1.5 hour more than Cathy's

Juan

distance = d

speed = 4

time = t + 1.5

d = 4 * (t+1.5)

Cathy

distance = d

speed = 5

time = t

d = 5 * t

5t = 4t + 6

t=6 hours (Cathy's time)

d = 5 * 6 = 30 miles