Genny travels from one elementary school to another and back at a rate of 20 mph one way and 30 mph the other way. What is her average rate of speed for both tr

Question

Genny travels from one elementary school to another and back at a rate of 20 mph one way and 30 mph the other way. What is her average rate of speed for both trips?

Answer 1

the distance does not matter because it is the same both ways

pick a distance of 60 miles (only because 60 is divisible by 20 and by 30)

60=20*t

60=30*t

60/20=3 hours to the school

60/30=2 hours from the school

total distance=rate*total time

60+60=rate*(3+2)

120=rate*5

rate=120/5

rate=24 mph is the average speed

people make the mistake of adding 20 and 30 and dividing by 2 to get 25 which is totally incorrect

suppose the distance is 12 miles

12=20*t

12=30*t

12/20=t=3/5 hours

12/30=t=2/5 hours

total distance=rate*total time

24=rate*[(2/5)+(3/5)]

24=rate*1

rate=24 mph again

if you are familiar with what is called the harmonic mean you can get the answer very quickly...

here is the simplified version for 2 rates...

(2*rate1*rate2)/(rate1+rate2)

(2*20*30)/(20+30)=1200/50=120/5=24 mph again