If (w) workers can finish a job in (h) hours, assuming a constant rate, how many hours would it take to complete the job with 1 less worker in terms of (w) and (h)?

Question

jigglypuff314 · Answer

Options... if you need it
A. $$\frac{ w }{ w-1 }$$B. $$\frac{ (w-1)h }{ w }$$C. $$\frac{ w(w-1) }{ h }$$D.$$\frac{ h }{ w(w-1) }$$E. $$\frac{ wh }{ w-1 }$$

anonymous · Answer

try doing it with numbers first, rather than $2$ workers and $h$ hours
i.e. try it with say $4$ workers take $5$ hours to do the job, how long would it take $3$ workers

raden · Answer

it is an inverse proportional

w ---> h
w-1 ---> x

solve for x :
w/(w-1) = x/h

jigglypuff314 · Answer

i.e. try it with say 4 workers take 5 hours to do the job, how long would it take 3 workers
in the case of ^ would it be  20/3 = 6.66hr?

anonymous · Answer

$4$ workers take $5$ hours to do the job
their combines rate is $\frac{4}{5}$ of a job per hour, so each worker does $\frac{1}{20}$ of the job per hour
therefore $3$ workers will do $\frac{3}{20}$ of a job per hour, it will take them $\frac{20}{3}$ hours to complete the job
your answer is right, except i wouldn't use the decimal, leave it as a fraction

jigglypuff314 · Answer

ohhh, okay, thank you! :)

anonymous · Answer

now replace the $4$ by a $w$ and the $5$ by an $h$ and redo exactly what you did above, using letters instead of numbers
in any case that is how i solved it

phi · Answer

radeng has the right idea.  To add some details:

It take w people working h hours  to finish 1 job
in other words,  1 job requires  w*h man-hours

if you have w-1 people, working for an unknown amount of time t
(w-1)*t  =  1 job or

(w-1) *t = w*h
solve for t:
t = w h/(w-1)

jigglypuff314 · Answer

Thanks you all! :D
your comments helped me a lot <3
I wish I could give you all medals :3

ybarrap · Answer

All explanations above are fantastic. Just one additional note. Look at your options. The units should be "hours.". Also, with 1 less worker, the amout of time to do the job should be "longer." There is only one option that makes sense. This is using  a different kind of logic that the ones here, but sometimes helpful for tests.