Lisa can make a costume twice as fast as Justin can. If they both work together, they can make it in 8 hours. How long will it take Justin to make the costume if he works alone?

Hi,

Concept: This is work & time related problem which can be solved in their inverse proportions.

Let Lisa can do a work in x hours.

Lisa's one hour work = 1 / x

According to the problem, Justin can do the same work in 2x hours.

Justin's one hour work = 1 / (2x)

Now, we shall find both 1 hour work just by adding their 1 hour's work.

Both 1 hour's work = (1 / x) + [1 / (2x) ] = 3 / (2x)

Full works time = (2x / 3) hours.

Again, according to the problem,

2x / 3 = 8

or, x = 12 hours.

Hence Justin will take 2x = 24 hours to complete work as alone.