Question

3. Together, Stan and Eli can mow a lawn in 3 hours. It would take Eli 5 hours to do it alone. How long would it take Stan alone?

Answer 1

Answer: It would it take 7.5h for Stan to do it alone.

Step-by-step explanation

Given

• Stan and Eli can mow a lawn in 3 hours.

,

• It would take Eli 5 hours to do it alone.

,

• How long would it take Stan alone?​

Procedure

Eli does 1/5 of the work per hour, while Stan and Eli do 1/3 of the work per hour. Assuming that their per-hour rates are additive (they never get in each other's way), we can build the following relation, in which t is the time of Stan doing it alone:

`(1)/(t)+(1)/(5)=(1)/(3)`
`(1)/(t)=(1)/(3)-(1)/(5)`
`(1)/(t)=(5-3)/(15)`
`(1)/(t)=(2)/(15)`

Getting the reciprocal of both sides:

`(t)/(1)=(15)/(2)`
`t=(15)/(2)\approx7.5h`