Sara can weed a garden in 30 minutes. When her brother Hamdan helps her, they can weed the same garden in 20 minutes. How long would it take Hamdan to weed the garden if he

worked by himself?

a. Write an expression for Hamdan's rate, using n for the number of hours he would take to

weed the garden by himself.

b. Write an equation to show the amount of work completed when they work together.

c. How long would it take Hamdan to weed the garden by himself?

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facundo3141592 facundo3141592 · Answer 1 · 2021-06-22T02:48:53+02:00

Answer:

Let's define:

S as the rate at which Sara can weed a garden.

We know that:

S*30min = 1 garden

And let's define H as the rate at which Hamdan can weed a garden, we know that when they work together, they can complete the job in 20 minutes, then

(S + H)*20min = 1 garden

a) Here we get:

H*n = 1 garden

where n is the number of hours that he would take (note that in two previous equations we have minutes, so we need to use a change of units)

b) The equation is

(S + H)*20min = 1 garden

c) ok, we know two things:

(S + H)*20min = 1 garden

S*30min = 1 garden

first, let's convert both times to hours:

60 min = 1 hour

then:

30 min = (30/60) hours = 0.5 hours

20 min = (20/60) hours = 0.33 hours

Then the equations become:

(S + H)*0.33 hours = 1 garden

S*0.5 hours = 1 garden

Le's solve the second equation for S:

S = (1 garden /0,5 hours) = 2 gardens/hour.

Now we can replace this in the other equation to get:

(2 garden/hour + H)*0.33 hours = 1 garden

2 garden/hour + H = (1 garden)/(0.33 hours) = 3 gardens/ hour

H = 3 gardens/hour - 2 gardens/hour = 1 gardens/hour

This means that the rate of Hamdan is 1 gardens/hour, so he can weed a garden in one hour.

Then:

(1 garden/hour)*n = 1 garden

n = ( 1 garden)/((1 garden/hour)) = 1 hour