Answer: 28.7 minutes
Step-by-step explanation:
Terrel: [tex]\dfrac{1}{69}[/tex] of job per minute
Wife: [tex]\dfrac{1}{49}[/tex] of job per minute
Together: [tex]\dfrac{1}{x}[/tex] of job per minute
Terrel + Wife = Together
[tex]\dfrac{1}{69}+\dfrac{1}{49}=\dfrac{1}{x}[/tex]
[tex]\dfrac{1}{69}(69*49*x)+\dfrac{1}{49}(69*49*x)=\dfrac{1}{x}(69*49*x)[/tex]
49x + 69x = 69 * 49
118x = 3381
x = 28.7
Time required to complete the work done when working together is equals to 28.7 minute( round to nearest tenth).
" Work done defined as the product of time taken to the rate of work ."
According to the question,
'x' represents time take to complete the work when working together
Terrel complete his work = 69 minutes
Work done by Terrel in 1 minutes = [tex]\frac{1}{69}[/tex]
Wife complete his work = 49 minutes
Work done by Wife in 1 minutes = [tex]\frac{1}{49}[/tex]
As per the condition given of working together,
[tex]\frac{1}{69 }+ \frac{1}{49} =\frac{1}{x} \\\\\implies\frac{49 + 69}{3381}=\frac{1}{x} \\\\\implies x= \frac{3381}{118} \\\\\implies x= 28.65[/tex]
x = 28.7minutes ( round to the nearest tenth)
Hence, time required to complete the work done when working together is equals to 28.7 minute( round to nearest tenth).
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