Question

Twin brothers, Andy and Brian, can mow their grandparent's lawn together in 60 minutes. Brian could mow the lawn by himself in 22 minutes more than it would take Andy. How long would ittake each person mow the lawn alone?lespleesIt would take Andy minutes to mow the lawn by himself(Simplify your answer.)It would take Brian minutes to mow the lawn by himself(Simplify your answer.)

Answer 1

STEP - BY - STEP - EXPLANATION

What to find?

The time taken for each person to mow the lawn alone.

Given:

Time take for the two to mow the lawn together = 60 minutes.

Brian could mow himself 22 minutes more than it would take andy.

Let x be the time taken for Andy to mow the lawn.

Let x + 22 be the time taken for Brian to mow the lawn.

Step 1

Form the equation.

`((1)/(x)+(1)/(x+22))*60=1`

Step 2

Divide both-side of the equation by 60.

`(1)/(x)+(1)/(x+22)=(1)/(60)`

`(x+22+x)/(x(x+22))=(1)/(60)`
`(2x+22)/(x^2+22x)=(1)/(60)`

Step 3

Cross-multiply.

`x^2+22x=60(2x+22)`

Step 4

Open the parenthesis.

`x^2+22x=120x+1320`
`x^2+22x-120x-1320=0`
`x^2-98x-1320=0`

Step 5

Solve the above using factorization method.

`\begin{gathered} x^2-110x+12x-1320=0 \\ \\ x(x-110)+12(x-110)=0 \\ \\ (x-110)(x+12)=0 \end{gathered}`

Either (x-110) = 0 or x+12 =0

x =110 or x =-12

Since there is no negative timing, we will consider only the positive value.

Hence, x=110

Therefore,

The time taken Andy to mow = 110 minutes.

The time taken for Brian to mow = x+ 22 = 110+22 = 132

ANSWER

It takes Brian 132 minutes to mow the lawn himself.

It takes Andy 110 minutes to mow the lawn himself.