x is 7.5 hours
Step-by-step explanation:
Ben, Tim, and Sam have to do a certain job
We need to find x
∵ Ben can finish the job in 5 hours
∴ The rate of Ben = [tex]\frac{1}{5}[/tex]
∵ Tim can finish the job in 6 hours
∴ The rate of Tim = [tex]\frac{1}{6}[/tex]
∵ Sam can finish the job in x hours
∴ The rate of Sam = [tex]\frac{1}{x}[/tex]
They will working together to finish the job in two hours, that means the sum of their rate is equal to 1/2
∵ They can finish the job in 2 hours if they work together
∴ [tex]\frac{1}{5}+\frac{1}{6}+\frac{1}{x}=\frac{1}{2}[/tex]
To add the fractions find the LCM for all denominators to make all fractions with same denominators
∵ The LCM of 5, 6 ans x is (5 × 6 × x) = 30 x,
- Divide it by each denominator to find the new numerators
∵ 30 x ÷ 5 = 6 x , 30 x ÷ 6 = 5 x , 30 x ÷ x = 30
- Change all the denominators to 30 x and then write the new
numerators of each fraction
∴ [tex]\frac{6x}{30x}+\frac{5x}{30x}+\frac{30}{30x}=\frac{1}{2}[/tex]
Add the numerators and put the sum over 30 x
∵ [tex]\frac{11x+30}{30x}=\frac{1}{2}[/tex]
- By using cross multiplication
∴ 2(11 x + 30) = 1(30 x)
- Simplify the both sides
∴ 22 x + 60 = 30 x
- Subtract 22 x from both sides
∴ 60 = 8 x
- Divide both sides by 8
∴ 7.5 = x
∴ The value of x is 7.5 hours
x is 7.5 hours
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