Respuesta :
Answer:
It takes 60 hours for Alex to complete the job alone.
Step-by-step explanation:
Given:
Number of hours Brandon alone can finish job =20 hours
Let the number of hours required by Alex alone to complete the job be 'x' hrs.
We need to find the number of hours required by Alex alone to complete the job.
Solution:
Now we can say that;
Rate at which Alex can complete the job alone = [tex]\frac1x[/tex] job/hour
Rate at which Brandon can complete the job alone = [tex]\frac{1}{20}[/tex] job /hour
Also Given:
Number of hours required for both to complete the job = 15
So rate of both complete the job = [tex]\frac{1}{15}[/tex] job/hour
Now we can say that;
rate of both complete the job is equal to sum of Rate at which Alex can complete the job alone and Rate at which Brandon can complete the job alone.
framing in equation form we get;
[tex]\frac1x+\frac{1}{20}=\frac{1}{15}[/tex]
Now taking LCM for making the denominators same we get;
[tex]\frac{20}{20x}+\frac{x}{20x}=\frac{1}{15}[/tex]
Now denominators are common so we will solve the numerators.
[tex]\frac{20+x}{20x}=\frac{1}{15}[/tex]
Now Using cross multiplication we get;
[tex]15(20+x)=20x[/tex]
Applying Distributive property we get;
[tex]15\times20+15\times x =20x\\\\300+15x=20x[/tex]
Combining like terms we get;
[tex]300=20x-15x\\\\300=5x[/tex]
Now Dividing both side by 5 we get;
[tex]\frac{300}{5}=\frac{5x}{5}\\\\x=60\ hrs[/tex]
Hence It takes 60 hours for Alex to complete the job alone.
