Question

Working alone, Bill can paint a house in 4 hours. When Tom helps, the job takes 2.5 hours. If tom worked alone, how long would it take him to paint the house ?

Answer 1

Bill's rate is 1 house / 4 hours = 1/4 house per hour.

Tom's rate is
`t`

Bill and Tom's combined rate
`(t + 1/4)` satisfies


`2.5 = 1 / (t + 1/4)`


`2.5 (t+1/4) = 1`


`t + 1/4 = 1/2.5`


`t = 11/2.5 - 1/4 =8/20 - 5/20= 3/20`

So it takes Tom
`(20)/(3)` hour (6 hours 40 minutes) to paint a house

Check:

[/tex]3/20 + 1/4 =3/20 + 5/20 = 8/20 quad[/tex] 8 houses per twenty hours, 2.5 hours per house
`\quad\checkmark`

Answer 2

6.7

Explanation:

Bill = 1 house / 4 hours,

Tom = 1 house / x hours,

Both = 1 house / 2.5 hours,

Here is the equation: (1/4 + 1/x) = (1/2.5)=20/3=6.67 round to the nearest tenth is 6.7 The answer is 6.7 hours.