math algebra

Question

The time T it takes to drive from Houston to Atlanta is inversely proportional to the driver's average speed, S . If it takes a driver 15 hours to drive to Atlanta at an average speed of 60 miles per hour, how many hours would it take to drive to Atlanta at 75 miles per hour?

Answer 1

From the first sentence, you can write the equation

 

T = k/S, where k is the constant of proportionality.

 

From the second sentence, T = 15 hr while S = 60 mi/hr. If you plug these into this equation and then solve for k, you will get

 

15 = k/60  ⇒  k = 15 · 60 = 900.

 

To answer the question, plug S = 75 and k = 900 into the first equation, then solve for T:

 

T = 900/75 = 12 hours.