Question

Mr. Jones jogs the same route each day. The amount of time he jogs is inversely proportional to his jogging rate.

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

4 mph for 2.5 hours and 6 mph for 3.75 hours


3 mph for 2 hours and 4.5 mph for 3 hours


4 mph for 2.5 hours and 5 mph for 2 hours


4 mph for 2.5 hours and 3 mph for 3.5 hours

Answer 1

Answer is option C

Mr. Jones jogs the same route each day. The amount of time he jogs is inversely proportional to his jogging rate.

$time= \frac{k}{rate}$

k is the constant of proportionality

We check with each option and identify which option gives us same K value

(a) 4 mph for 2.5 hours and 6 mph for 3.75 hours

$2.5= \frac{k}{4}$ so k = 10

$3.75= \frac{k}{6}$ so k = 22.5

K values are not same

(b) 3 mph for 2 hours and 4.5 mph for 3 hours

$2= \frac{k}{3}$ so k = 6

$3= \frac{k}{4.5}$ so k = 13.5

K values are not same

(c) 4 mph for 2.5 hours and 5 mph for 2 hours

$2.5= \frac{k}{4}$ so k = 10

$2= \frac{k}{5}$ so k =10

K values are  same .

Answer is option C