Irene drove to work at a rate off speed of 60mph and returned home at a speed of 40 mph. If her total driving time was 1 hour, what was the total distance she

Question

 Irene on the same road each time, and covered both the total distance in the time of 1 hour.

Answer 1

distance=rate*time

d=rt

let t be in minutes

d=60t  (to work)

d=40(60-t)  (return home)

both equations equal d so set them equal to each other

60t=40(60-t)

60t=2400-40t

60t+40t=2400

100t=2400

t=24 minutes spent driving to work

24 minutes=24/60 hours=2/5 of an hour driving to work and 3/5 of an hour driving home

d=r*t

d=60*(2/5)

d=120/5=24 miles to work and 24 miles back home again

to confirm this...

d=r*t

d=40*(3/5)

d=120/5=24 miles back home again

She traveled 24+24=48 miles altogether

By the way her average speed is not 50 mph.

There are two ways to look at this.

d=r*t

48=r*1

48/1=r

r=48 mph

If you understand what is called the harmonic mean, then you can calculate the average speed in the following manner:

(2*R1*R2)/(R1+R2) where R1 and R2 are the two speeds

(2*60*40)(60+40)=4800/100=48 mph

Answer 2

Average (Mean) speed is = (60 mph+ 40 mph)/2= (100 mph)/2= 50 mph

 

If she drives at 50 m/h as average speed and Speed= d/t then d= V*t= 50 m/h * 1 h, then in 1 hr she  covered a distance of 50 miles.