Question

max cycles at a speed of 15 mph. He cycles 12 miles from home to school.                  If he increases the sped by 5 mph, how much faster will he reach his school?

(if you answer the question please show how you got it, please.)

Answer 1

the cyclist would be going 20 mph after increasing his speed by 5 mph. but we would need to know how fast it took him to get to school when he was going to school to figure out how long it would take him to get to school. the distance 12 miles would not get shorter with max going faster, it would stay the same. so you would need to know how long it was taking him to get to school before i could do the math to figure out how fast he would get to school with his increased speed.

Answer 2

First of all, you're not really asking "How much faster ?".
That would be "5 mph faster".
You're really asking "How much sooner ?"

At 15 mph, the trip takes him 12/15 = 4/5 hour.

At 20 mph, the trip takes him 12/20 = 3/5 hour.

The time saving is (4/5 - 3/5) = 1/5 hour .

= 12 minutes

Notice that by changing to 5/4 of his original speed,
he changed the trip to 4/5 of the original time.
It always works out like that ... reciprocally.