Efren leaves home at 9am and walks 4 miles per hour. His brother, gregory leaves half an hour later and runs 8.5 miles per hour in the same direction as efren. Predict the time at which gregory will catch up to efren

Gregory will catch up Efren after 26 minutes 40 seconds.

Explanation:

Distance traveled = Speed x Time

Speed of Efren = 4 mi/h

Speed of Gregory = 8.5 mi/h

Let the time of catch up be t hours.

Time of journey of Efren before catch up = (t+0.5) hours, since he starts before half hour.

Distance traveled by Efren = 4 x (t+0.5) miles

Time of journey of Gregory before catch up = t hours.

Distance traveled by Gregory = 8.5 x t miles

If they catch up the distance traveled by them is same, so equating both distances.

4 x (t+0.5) = 8.5 x t

4.5t = 2

t = 0.44 hours = 26.67 minutes = 26 minutes 40 seconds.

So Gregory will catch up Efren after 26 minutes 40 seconds.