Question

A group of hikers walked 2 1/4 km in 3/4 hour.The distance here varies directly with time. What is the constant of variation?

Answer 1

The distance depends on the time.

So now we need to find the constant of variation or the constant of proportionality.

To do so we must find y(the dependent variable) and x(the independent variable).

To find the constant(k) we must find y/x

Since y/x=k

Then 2.25/.75=k

k=3

Answer 2

k = 3

let distance walked be d and time be t

since distance varies directly with time then

d = kt ← k is the constant of variation

k = $\frac{d}{t}$

note that 2 $\frac{1}{4}$ = $\frac{9}{4}$, hence

k = $\frac{9}{4}$ / $\frac{3}{4}$ = 3