At 8:00 AM a bicyclist departed city A, heading towards city B at a rate of 20 km/h. After traveling for 4 hours he stopped for an hour break. At the same time, a biker left city A traveling in the same direction at the rate of 50 km/h. How long will it take the biker to catch up to the cyclist?

2 hours and 40 minutes

Step-by-step explanation:

After 4 hours, 1st person went 20 * 4 = 80 km

+1 hours rest

So now after total 5 hours (when 2nd one started), 1st one is 80 km ahead.

2nd bicyclist rate is 50

1st bicyclist rate is 20

So, for each hour, 2nd bicyclist advances 50 - 20 = 30 kilometers

How long will it take him, at this rate, to catch up 80 kilometers?

Simple!

30 km catch up every hour, so

80/30 = 2 2/3rd hours

That would be 2 hours 40 minutes to catch up