Solve using distance = rate x time
mike left home on his bicycle at 10: 00 a. m., traveling at 50 m/h. at noon, he arrived at his destination. how many miles did he drive?

The rate is speed which 50m/h. so he left the home at 10:00 and arrived at noon which 12:00pm so the difference is 2 hours which means he took 2 hours to get there.
to find the distance. 
D=RxT = 50 x 2 = 100mile

Distance = Rate * Time

The rate he is going at is 50 mph
The time it took is 10 am to 12 pm. That is 2 hours.

Distance = 50 mph * 2 hr

Distance = 100 miles

Mike drove 100 miles.