Question

A car is moving at a fixed speed. The distance D that the car covers is then directly proportional to the time T it moves.

If D=20 miles when T=15 minutes, write a proportion to find D for T=20 minutes

Answer 1

We were told that the distance $D$ is directly proportional to the time $T$.

We write this mathematically as,

$D\propto T$

We can now introduce our constant of variation and write the equation for the direct equation as;

$D=kT$

where $k$ is the constant of variation or constant of proportionality.

We substitute $D=20$ and $T=15$, in to the equation of variation to obtain the constant of proportionality.

That is;

$20=k\times15$

This implies that,

$\frac{20}{15}=k$

This simplifies to give us,

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

Now our equation of proportion becomes,

$D=\frac{4}{3}$

When T=20

$D=\frac{4}{3}\times20$

$D=\frac{80}{3}$

Writing this as a mixed number we obtain,

$D=26\frac{2}{3}$

This can also be rewritten as

$D=26.67$ correct to one decimal places.

Therefore the care covers $26.67$ miles in $20$ minutes.