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*15`

This implies that,

`(20)/(15)=k`

This simplifies to give us,

`k=(4)/(3)`

Now our equation of proportion becomes,

`D=(4)/(3)`

When T=20

`D=(4)/(3)*20`

`D=(80)/(3)`

Writing this as a mixed number we obtain,

`D=26(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.