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Question

Sam drove for 2 hours at 45 mph. He has the same distance remaining. How fast should he drive to make his average speed 60 mph?

 

Sam drove for 2 hours at 45 mph. He has the same distance remaining. How fast should he drive to make his average speed 60 mph?

Answer 1

2 hours at 45 mph gives a distance of 90 miles

he has another 90 miles to travel

total distance=rate*(total time)

his average speed must be 60 mph

180=60*(2+t) where t is the amount of time he has to travel the other 90 miles

180=120+60t

180-120=60t

60=60t

t=60/60

t=1 hour

Sam must travel 90 miles in 1 hour, thus Sam must travel 90 miles per hour to have an average of 60 mph

90 mph is the answer

 

you can check by using the harmonic mean if you understand what it is:

(2*45*90)/(45+90)=8100/135=60

 

you can also find the answer using the harmonic mean:

(2*45*R)/(45+R)=60

(2*45*R)=60*(45+R)

90R=2700+60R

90R-60R=2700

30R=2700

R=2700/30

R=90 mph must be Sam's speed for the other 90 miles to average 60 mph

 

Answer 2

If Sam drives for 2 hours at 45 miles per hour. He will go 90 miles. 

The second half of the problem says nothing about time. He would simply need to average a speed of 60mph.