Question

the time, t, required to drive to a certain distance varies inversely with the speed, r. if it takes 12 hours to drive the distance at 60 miles per hour, how long will it take to drive the same distance at 85 miles per hour ?

A. about 7.08 hours
B. about 5.00 hours
C. about 1.42 hours
D. about 8.47 hours

Answer 1

T = k/R  where k is the constant of variation, T=time and R=speed.
Plug in the given values:-
12 = k/60
k = 12*60 = 720
So the equation of variation is T = 720/R

At 85 mph we have

T = 720 / 85 =  8.47 hours (answer)

Answer 2

The correct option is Option D: it will take 8.47 hours to drive.

What is inversely proportional?

Inversely proportional is the relation between two values when one value increases another value decreases .

if x is inversely proportional to y then,

x∝1/y

⇒x=k/y where k is the proportionality constant.

Here time t is inversely proportional to the speed r

t∝1/r

⇒t=k/r where k is the proportionality constant.

given, that 12 hours is needed to cover a certain distance at speed 60 miles per hour.

t1=12hours

r1=60 miles per hour

According to the inversely proportionality condition

t1=k/r1

⇒12=k/60

⇒k=720

Now we have to derive the time t2 taken to cover the same distance at a speed of 85 miles per hour.

r2=85 miles per hour

t2=k/r2

⇒t2=720/85

⇒t2= 8.47 hours

Therefore it will take 8.47 hours to drive.

Learn more about inversely proportional

here: https://brainly.com/question/17447335

#SPJ2