Question

Martina leaves home at 9 am, bicycling at a rate of 24 mi/h. Two hours later, John leaves, driving at at rate of 48 mi/h. At what time will john catch up with Martina?

Answer

M = Martina’s distance from home at time t, in hour.
M = 24t

J = John’s distance from home at time t, in hour.
J = 48(t – 2)

Why (t – 2)? because, John started 2 hours later.

Thus, when ” john catch up with Martina” means that their distance from home is equal. Thus,

24t = 48(t – 2)
t = 2t – 4
or t = 4.

This means 4 hours from the time Martina’s leaves home, John, would have caught up with her. The time is just 4 hours after 9 am, i.e, 1 pm.