At 11:00 a.m., John started driving along a highway at constant speed of 50 miles per hour. At what time will Jimmy catch up with John?

Question

At 11:00 a.m., John started driving along a highway at constant speed of 50 miles per hour. A quarter of an hour later, Jimmy started driving along the same highway in the same direction as John at the constant speed of 65 miles per hour. At what time will Jimmy catch up with John?

Answer 1

Let \(\mathrm{t}\) be the number of hours, from 11:00 am, when Jimmy catches up with John. The time that Jimmy will have to drive to catch up with John is \(\mathrm{t}-1 / 4\) : he starts a quarter of an hour late. Whe Jimmy catches up with John, they would have traveled the same distance. Hence \(50 t=65(t-1 / 4)\)
Solve for \(t\)
\(50 t=65 t-65 / 4\)
\(t=65 / 60=1.083\) hours \(=1\) hour and 5 minutes
Jim will catch up with John at
11:00 am \(+1\) hour, 5 minutes \(=12: 05 \mathrm{pm}\)