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 $\frac{20}{3}$ 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

Answer:

6.7

Step-by-step 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.