Question

Wangari plants 12 trees every 3 hours. Write an equation that relates the number of trees Wangari plants (p) and the time she spends planting them (h) in hours.

Answer 1

Answer:
`p=4h`

Explanation:

The equation of direct variation is given by:

`y=kx`

where, x= independent variable

y= dependent variable

k is the constant of proportionality.

Let the number of trees Wangari plants is denoted by p and the time she spends planting them is denoted by h ( inhours).

here , independent variable = h

dependent variable = p

Since time ∝ Number of plants planted.

So by using direct variation equation , we get

`p=kh` (1)

According to the given statement : Wangari plants 12 trees every 3 hours.

So we have

`12=k(3)\\\\\Rightarrow k=(12)/(3)=4`

Put value of k in (1) , we get

`p=4h`

Hence, the required equation that relates the number of trees Wangari plants (p) and the time she spends planting them (h) in hours:

`p=4h`

Answer 2

`p = 4h`

Explanation:

The equation of straight line is given by:

`y=mx`

where, m is the slope or rate of the line.

As per the statement:

Wangari plants 12 trees every 3 hours.

By definition of unit rate:

`\text{Unit rate per hour} = (12)/(3) = 4` trees.

⇒
`m = 4`

We have to find an equation that relates the number of trees Wangari plants (p) and the time she spends planting them (h) in hours.

then;

`p = 4h`

where, p represents the plant trees and the time she spends planting them in h hours

Therefore,
`p = 4h` an equation that relates the number of trees Wangari plants (p) and the time she spends planting them (h) in hours.