word problem?

Question

Winston can mow his dads lawn in 1 hour less than it takes his brother Will. If they take 2 hours to mow it when working together then how long would it take Winston working alone?

Answer 1

let t be the time it takes Winston to mow the lawn alone. Then t + 1 is the time it takes him to mow the lawn alone

in 1hr, Winstion can mow the1/t of the lawn
in 1hr, his brother can mow 1/(t+1) of the lawn

they work together, mow the lawn in 2hrs

1/t*2 + 1/(t+1)*2 = 1
2/t + 2/(t+1) = 1
2t + 2 + 2t = t^2 + t
4t + 2 = t^2 + t
0 = t^2 - 3t - 2

use quaratic formula and you'll get t =~3.56155 hrs

so Winston can mow the lawn in 3.56155 hrs alone

Answer 2

Let x = no of hrs it will take for Will to mow the lawn alone
x -1 = no of hrs it will take for Winston to mow the lawn alone

2 = no of hrs it will take the brothers to mow the lawn together

1/x + 1/(x-1) = 1/2
[ x + x - 1] / x ( x - 1) = 1/2

2 (2x - 1) = x (x - 1)

4x - 2 = x^2 - x

x^2 - 5x + 2 = 0

Use Quadratic Formula to solve for x

Will = [5 + sqrt(17)]/2 = 4.56 hrs

Winston = 3.56 hrs

Answer 3

get what you know..
what you don't know use "x"
then it turns into a algebraic^ expression