Alegbra question

Question

Barry can do a certain a job in 7 hours, whereas it takes Samuel 11 hours to the same job. How long would it take them to do the job working together?

Answer 1

This is a rate times time problem. The rate for Barry is 1 job per 7 hours and the rate for Samuel is 1 job per 11 hours. They each work for H hours. The equation to be solved is (1/7)H + (1/11) H = 1.

Multiply each side by the common denominator or 77.

11 H + 7 H = 77

18 H = 77

H = 77/18 or 4 5/18 hours

or 4 hours and (5/18 )(60) for minutes and 12 (60)/18 for seconds (the 12 remainder as a fraction was 12/18)

4 hours 16 minutes 4 seconds.

Answer 2

(1/11) (1/7) = (1/x)

(11+7)/77=1/x

x=77/18 = approximately 4.3 hrs

Now, 2 things about this answer:

1st: this method ALWAYS works for work problems and it is worth remembering this process for speed in answering such questions.

2nd: the reason it works is that the fractions are rates, e.g. 1/11 is i job per 11 hrs

When you multiply this rate by hours you get amount of job done in that number of hours

1/11 * x hours is the amount of the job Samuel does in x hrs.

Therefore (1/11)*x + (1/7)x = 1 i.e. the amount of the job Sam does plus the Barry does is the whole job.

Answer 3

Barry can do a certain a job in 7 hours, whereas it takes Samuel 11 hours to the same job. How long would it take them to do the job working together?

Barry can do the job in 7 hours. in 7 X 11 = 77 hours, Barry could do 11 of the jobs.

Sam can do the job in 11 hours. in 11 X 7 = 77 hours, Sam could do 7 of the jobs.

So in 77 hours, together they could do 18 of the jobs. But to do just 1 job, they would only need 77 ÷ 18 hours to do it or 4.28 hours.

The way to set this type of problem up is to use fractions.

The numerator has a multiplication of the two times and the denominator has an addition of the two times. Then solve:

7 X 11

7 + 11 = 77 ÷ 18 = 4.28