Question

Steve can paint a room three times as fast as Billy. When they work together, Steve and Billy can paint a large room in 4 hours. How many hours would it take Billy to paint it by himself?

Answer 1

let x be the rate of Steve working, then the rate of Billy will 3x
the whole job be 1
1/(x+3x) = 4
x = 1/16
3x = 3/16 hr. => Billy paint by himself

Answer 2

Answer: 16 hours

Explanation:

Let x be the number of hours taken by Billy to paint a room by himself.

Speed of Billy
`=\frac{\text{work}}{\text{time}}=(1)/(x)`

Since, Steve can paint a room three times as fast as Billy.

Then , speed of Steve =
`3*(1)/(x)=(3)/(x)`

If they worked together to paint a large room in 4 hours the we have the following equation:-

`\Rightarrow(1)/(x)+(3)/(x)=(1)/(4)\\\\\Rightarrow(3+1)/(x)=(1)/(4)\\\\\Rightarrow(4)/(x)=(1)/(4)\\\\\Rightarrow x=4*4=16`

The time taken by Billy to paint the large room by himself = 16 hours