Question

You ride your bike x miles per hour up a mountain for 45 minutes. On the way down the mountain, you ride your bike for 4 miles per hour faster. It takes 20 minutes to ride your bike down the mountain. How far did you ride your bike in total?

Answer 1

Speed of bike up-mountain= x mph

Time of bike ride up-mountain= 45 minutes or 45/60 hours

Distance of bike ride up-mountain= x*45/60=3x/4 miles

Speed of bike down-mountain= (x+4) mph

Time of bike ride down-mountain= 20 minutes or 20/60 hours

Distance of bike ride down-mountain= (x+4)*20/60=(x+4)/3 miles

As the distance of bike ride up-mountain and down-mountain is the same—3x/4 miles=(x+4)/3 miles

3x/4=(x+4)/3

9x=4x+16

5x=16

x=16/5=3.2 mph

Distance of bike ride up-mountain= 3.2*45/60=2.4 miles

Distance of bike ride down-mountain= 7.2*20/60=2.4 miles

Total distance of bike ride both up-mountain and down-mountain=4.8 miles in 65 minutes