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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?

Respuesta :

Dimples26ld
 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
JeanaShupp

Answer: 16 hours

Step-by-step explanation:

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

Speed of Billy[tex]=\frac{\text{work}}{\text{time}}=\frac{1}{x}[/tex]

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

Then , speed of Steve =[tex]3\times\frac{1}{x}=\frac{3}{x}[/tex]

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

[tex]\Rightarrow\frac{1}{x}+\frac{3}{x}=\frac{1}{4}\\\\\Rightarrow\frac{3+1}{x}=\frac{1}{4}\\\\\Rightarrow\frac{4}{x}=\frac{1}{4}\\\\\Rightarrow x=4\times4=16[/tex]

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