Sam left his school at 3: 05. he walked at a speed of 3.2 mph. 15 minutes later, al started running after him, and he caught up with sam 10 minutes later. what was al’s speed?

Let's look at what we know about Sam and Al.

Sam walked for 15 minutes before Al started running after him, then he walked for another 10 minutes while Al was trying to catch up to him. Therefore Sam walked a total of 25 minutes. We also know that he walked at a speed of 3.2mph. 
25/60 hours * 3.2miles per hour = 
5/12 hrs * 16/5 mph = 
80 / 60 miles = 
4/3 miles

I did the math in fractions instead of decimals because in this case, 4/3 is cleaner than 1.333333

Now lets look at what we know about Al. He ran for 10 minutes. We also know that he ran 4/3 miles since he caught up with Sam and that's how long Sam had walked. If we put this information into an equation we can solve for Al's speed:
10 minutes * x miles per hour = 4/3 miles
1/6 hr * x mph = 4/3 miles
x = 24/3 mph
x = 8 mph

Therefore, Al ran at 8mph.