You ride your bike x miles per hour up a mountain for 45 minutes. On the way down the mountain, you ride your bike 2 miles per hour faster. It takes 20 minutes to ride your bike down the mountain. How far did you ride your bike in total?

2 2/5 (or 2.4) miles.

Step-by-step explanation:

Your speed up the mountain =

x = distance / time = d / 3/4 where d is the distance travelled up the mountain. (its 3/4 because 45 minutes = 3/4 hour).

Coming down the mountain your speed

= x + 2 = d / 1/3 (the distance is also d travelling down).

Simplifying the 2 equations:

x = 4d/3

x + 2 = 3d

Substituting x = 4d/3 in the fist equation>

4d/3 + 2 = 3d

Multiply through by 3

4d + 6 = 9d

6 = 5d

d = 6/5 miles.

The total distance you rode = 2 * 6/5

= 12/5

= 2 2/5 miles.