2M/(M/20+M/25)

Question

If Teddy rides his bike to school at 20 mph and rides home the same way at 25 mph, what is his average speed in miles per hour? 

Answer 1

You use what is called the harmonic mean. You write it as 2/[(1/20)+(1/25)]. You use 2 in the numerator because there are 2 speeds.

2/[(1/20)+(1/25)]=2/[(5/100)+(4/100)]

2/(9/100)=2*100/9

200/9=22.222... mph is the average speed

I usually write it as 2*(speed1)*(speed2)/[(speed1)+(speed2)]

2*20*25/(20+25)=1000/45=200/9=22.222...

 

To illustrate this, suppose Teddy rides 50 miles to school at 20 mph and rides home 50 miles at 25 mph.

It takes Teddy 2.5 hours to ride to school and 2 hours to ride home.

He rides 50+50=100 miles and it takes him 2.5+2=4.5 hours.

What is his average speed ?

100 miles/4.5 hours=1000/45=200/9=22.222... mph

Answer 2

You can take the average of 20 and 25 to find the average speed in miles per hour.

 

The average would be:

 

(20 + 25) / 2 = 45/2 = 22.5 miles per hour