Question

The amount Troy charges to mow a lawn is proportional to the time it takes him to mow the lawn. Troy charges 30 to mow a lawn that took him 1.5 hours to mow.

​​Which equation models the amount in dollars, d, Troy charges when it takes him h hours to mow a lawn?

Answer 1

The amount Troy (D, in dollars) charges to mow a lawn is proportional to the time (H, in hours) it takes him to mow the lawn.

Hence, we can write
`\text{D = kH}` ......... (1), where k is a constant.

Now, given that Troy charges $30 to mow a lawn that took him 1.5 hours to mow.

So, from equation (1) we get

`{30 = 1.5\text{k}`

`\rightarrow \text{k = 20}`.

Therefore, equation (1) becomes

`\boxed{\bold{D = 20H}}` (Answer)