Average speed

Question

A dirtbiker must Circle a 5 mile track twice. His average speed must be 40 mph. On his first lap he averaged 25 mph. How fast must he travel during his
second lap to qualify? the teacher said the answer is 100 but gave no explination of how to arrive at the answer

Answer 1

distance=rate*time

total distance=average rate*total time

5=25t for the first lap

5=rt for the second lap

find the total time...

5/25=t

5/r=t

total time=5/25+5/r

total time=1/5+5/r

total time=(r+25)/5r

total distance=average rate*total time

10=40*(r+25)/5r

10=8(r+25)/r

10r=8(r+25)

10r=8r+200

10r-8r=200

2r=200

r=200/2

r=100 mph must be his speed for the second lap

you could have found the second rate by using the harmonic mean

(2*25*r)/(25+r)=40

50r=40(25+r)

50r=1000+40r

50r-40r=1000

10r=1000

r=1000/10

r=100 mph again

check:

5=25*t

5=100*t

5/25=t

5/100=t

1/5=t

1/20=t

1/5+1/20=4/20+1/20=5/20=1/4 hour for the total time

d=rt

total distance=average rate*total time

10=40*(1/4)

10=10

 

 

Answer 2

Fiona,

 

We can get the average speed (of two different speeds) by setting:

 

V(ave) = (V1 + V2)/2

 

Your problem states that the average speed is 40 mph and V1 (the speed on the 1st lap) was 25 mph.

 

Using these numbers we get:

 

40 = (25 + V2)/2 ⇒ 80 = 25 + V2, so:

 

V2 = 80 - 25 = 55 mph

 

This is the speed the racer needs to average on the second lap to qualify.