Answer:
2:21
Explanation:
You want the meeting time of two bikers traveling at 12 mph and 14 mph, closing a distance of 6 miles between them, when the first starts at 2:05, and the second starts at 2:09.
Gap to be closed
The first biker starts at 2:05 and peddles for 4 minutes before the 2nd biker starts. In that time, the distance traveled is ....
distance = speed × time
(12 mi/h) × (4/60 h) = 48/60 mi = 0.8 mi
The gap between the bikers has been reduced from 6 miles to 6 -0.8 = 5.2 miles by the time the second biker starts at 2:05 + :04 = 2:09 on the clock.
Time to close the gap
After the second biker starts at 2:09, the 5.2 mile gap between them is being closed at their combined rate of travel: 12 mph +14 mph = 26 mph. The time required to close that 5.2 mile gap is ...
time = distance/speed
time = (5.2 mi) / (26 mi/h) = 0.2 h = 0.2(60 min) = 12 min
Meeting time
The bikers will meet 12 minutes after the second biker starts, at ...
2:09 + :12 = 2:21
The bikers will meet at 2:21.
Graph
The attached graph shows equations for the distance from the 2nd biker's end of Main street (y1), and the distance the 2nd biker travels (y2). The value of x is the clock time in hours. It shows the two bikers meet at hour 2.35. That fraction of an hour is (0.35 h)×(60 min/h) = 21 min, so their meeting time is 2:21 on the clock. (They meet 2.8 miles from the 2nd biker's starting location.)