Julie drives 100 mi to Grandmother's house. On the way to Grandmother's,

Question

Julie drives 100 mi to Grandmother's house. On the way to Grandmother's, Julie drives half the distance at 34.0 mph and half the distance at 66.0 mph . On her return trip, she drives half the time at 34.0 mph and half the time at 66.0 mph . What is Julie's average speed on the way to Grandmother's house? What is her average speed on the return trip?

 

 

#2.3

ANSWERS: (a) 44.9 mph; (b) 50.0 mph

Answer 1

 

distance=rate*time

total distance=rate*total time

to Grandmother's...

50=34*t

50/34=t

t=25/17 hours for the first 50 miles

50=66*t

50/66=t

t=25/33 hours for the second 50 miles

total distance=50+50=100 miles

total time=25/17+25/33

total time=(825/561)+(425/561)=1250/561 hours

total distance=rate*total time

100=r*(1250/561)

r=(100)(561/1250)

r=56,100/1250

r=5610/125

r=1122/25

r=44.88 mph is the average speed (rounded it is 44.9 mph)

Note: If you are familiar with the simplified form of the harmonic mean you can solve the problem that way. If not, that's okay. You can look it up if you like.

(2*34*66)/(34+66)=4488/100=44.88 again

 

from Grandmother's house...

because the times are the same you simply add the 2 rates and divide by 2

(34+66)/2=100/2=50 mph is the average speed

d=r*t

100=34*t+66*t (the times are the same, t)

100=100*t

t=1 hour traveling at 34 mph and 1 hour traveling at 66 mph for a total of 2 hours traveling

d=r*t

100=r*2

r=100/2

r=50 mph is the average speed