Answer: A) 18.2 minutes B) 4.5 minutes. Step-by-step explanation: A) Maxine can mow one lawn in 24 minutes, so the rate of work is: 1/24 of the lawn per minute. Sammie can mow one lanw in 36 minutes, so the rate of work is: 1/36 of the lawn per minute. The amount of the lawn that each has left to lawn by the minute x is: Maxine = 1 -(1/24)*x Sammie = 1 - (1/36)*x we want to find the value of x such that: 2*(1 - (1/24)*x) = 1 - *(1/36)*x which means that the amount that Sammie has left is two times the amount that Maxine has left to mow. 2 - (1/12)*x = 1 - (1/36)*x 2 - 1 = (1/12 - 1/36)*x 1/0.055 = x = 18.2 by the minute 18.2 B) Similar to before, here the rates are: For Maxine, R = 1/6 For Sammie, R = 1/9 The amount they have left to mow by minute x is: Maxine = 1 - (1/6)*x Sammie = 1 - (1/9)*x We want to solve, similar to before. 2( 1 - (1/6)*x) = 1 - (1/9)*x 2 - (1/3)*x = 1 - (1/9)*x 2 - 1 = (1/3 - 1/9)*x 1 = (2/9)*x 1*9/2 = x = 4.5 So here the solution is 4.5 minutes. Hope this helps
