Rational Algebraic Expressions

Question

A mother does a general cleaning of the house every weekend. Her son, Josh, helps her do the cleaning. Normally, it takes her 3 hours to do the general cleaning. When josh helps her, the job takes only 2 hours. How long would it have taken Josh to do the general cleaning himself?

Answer 1

m=3 = 3 hours for mom alone

1/j + 1/m = 1/2

1/j + 1/3 = 1/2

1/j = 1/2 - 1/3 = 1/6

j= 6 hours for josh alone

if josh were exactly as fast as mom, together it would have taken half of 3 or 1.5 hours

since it took 2 > 1.5, you know josh is slower than mom

he's exactly twice as slow 1/6 = 1/2 x 1/3