Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can drive him 18 miles per hour faster and gets him to school in 12 minutes. How far (in miles) is it from Jeremy's home to school?

Let's say that the speed that Jeremy's father drives Jeremy through traffic is x. When there is no traffic, Jeremy's father drives 18 miles per hour faster than his speed in traffic, x. This would make the speed that Jeremy's father drives Jeremy to school without traffic, 18 / 60 + x. This is as it is 18 miles per hour faster, not 18 miles per minute faster.

Now recall the formula Speed = Distance / Time, or S = D / T. We want the distance here ( How far (in miles) from Jeremy's home to school ) so let's isolate D here in this formula,

S = D / T ⇒ D = S [tex]*[/tex] T - and as you know, the distance from Jeremy's home to school is the same, with or without traffic. So, we can consider case 1 : Jeremy's " distance traveled " in traffic, and case 2 : Jeremy's " distance traveled " without traffic, and make them equal to one another.

20 [tex]*[/tex] x = 12 [tex]*[/tex] ( 18 / 60 + x ),

20x = 3.6 + 12x,

8x = 3.6,

x = 0.45 - Now the distance is 20 [tex]*[/tex] x, and hence 20 [tex]*[/tex] 0.45 = 9 miles