What option gives possible rates and times for two of his jogs?

Question

The amount of time he jogs is inversely proportional to his jogging rate.

 

A. 6mph for 1.5 hours and 5mph for 1.25 hours

B. 5mph for 2 hours and 4mph 3 hours

C. 4mph for 2.25 hours and 6mph for 1.5

D. 4.5mph for 3 hours and 6mph for 4 hours 

Answer 1

His time(t) is inversely related to his speed(v). This gives us the following equation:

t = k/v

where k, the constant, also represents the distance he jogs.

 

Now let's make k the subject of our equation. We get

k = t x v

 

The option with both sets of time and rate, when multiplied, yielding the same number is the correct one. 

 

So the answer is C.

 

Answer 2

Since T is inversely proportionate to rate (R), means there is a constant such that T = k/R

 

This is the same as R * T = k

 

Assume the constant is the same for both joggers, their rate and time multiplied together must be the same.

 

This is true only for answer C,

 

4 mph for 2.25 hours => 4 * 2.25 = 9 mi

6 mph for 1.5 hours => 6 * 1.5 = 9 mi

Answer 3

The faster he jogs, the less time he takes.

Now look at each choice.

In which one does the rate increase and the time decrease?

Or in which one does the rate decrease and the time increase?

Notice the question asks for "two of his jogs." Two of the choices are correct.