Question

There are only two robots, tars and case aboard the nasa spacecraft. It takes tars 'x' hours to do a job that cars can do in 'y' hours. If tars operates alone for 'z' hours and is then joined by case until 100 such identical jobs are done, for how long will the two operate simultaneously?Pick one of the choices(100xy-z) / (x+y)y(100x-z) / (x+y)100y(x-z) / (x+y)none of the above

Answer 1

Tars take x hours to do a job

$\text {1 hour = }\dfrac{1}{x} \text { of the job}$

Cases take y hours to do a job:

$\text {1 hour = }\dfrac{1}{y} \text { of the job}$

Find the number of jobs done if Tars worked for z hours:

$\text {1 hour = }\dfrac{1}{x} \text { of the job}$

$\text {z hour = }\dfrac{z}{x} \text { of the job}$

Find the remaining job:

$\text {Remaining Job}= 100 - \dfrac{z}{x}$

Find the amount of job Tar and Case can do in 1 hour:

$\text {1 hour = } \dfrac{1}{x} +\dfrac{1}{y} = \dfrac{x + y}{xy}$

Find the number of hours need for both of them to finish the rest of the job:

$\text {Hours needed = } (100 - \dfrac{z}{x} ) \div (\dfrac{x + y}{xy})$

Convert divide fraction to multiplication fraction:

$\text {Hours needed = } \dfrac{100x - z}{x} \times \dfrac{xy}{x+ y}$

Cancel x as the common factor:

$\text {Hours needed = } \dfrac{y(100x - z)}{x + y}$

$\boxed { \boxed { \bolded { \text {Answer: } \dfrac{y(100x - z)}{x + y}}}}$

Answer 2

hey!

here is answer

let Tars take x hours to do a job

then 1 hour= 1/x of the job

cases take y hours to do a job

1 hour= 1/y

hence

number of jobs done if tars worked for z hours

1hour=1/x

z hour= z/x

see in. pic for. whole solution

hope it helps. thanks