Rational Expressions Applications

Question

Seth and Ted can paint a room in 3 hours if they work together. Because Ted is still an apprentice, if he were to work by himself, it would take him twice as long as it would take Seth working by himself. How long would it take Seth to paint the room by himself if Ted calls in sick?

Answer 1

1/s + 1/t = 1/3

t=2s

1/s + 1/2s = 1/3

multiply both sides by 6s to remove fractions

6+3 = 2s

s = 9/2 = 4 1/2 hours for seth to do it alone

ted takes 9 hours alone

together they do it in 3 hours

look at what happens in one hour

ted does 1/9 the job in one hour

seth does 1/(4 1/2)= 1/(9/2)= 2/9 the job in one hour

together in one hour they do 1/9 + 2/9 = 3/9 = 1/3 of the job

if they do 1/3 the job in 1 hour, together they can do the whole job in 3 hours