Question

Sue can shovel snow from her driveway in 40min. Tom can do the same job in 35min. How long would it take sue and tome to shovel the driveway if they worked together?

Answer 1

gimmick is to all the job 1 for one job, and each rate as a portion of the job
so if it takes sue 40 minutes her rate is 1/40 and likewise tom's rate is 1/35

to their comined rate is
\[\frac{1}{40}+\frac{1}{35}\] and you want to solve
\[(\frac{1}{40}+\frac{1}{35})t=1\] for t

Answer 2

a little practice and you will see that it is just the reciprocal of
\[\frac{1}{40}=\frac{1}{35}=\frac{35+40}{35\times 40}\]and do it quickly

Answer 3

in fact you could go right to
\[\frac{35\times 40}{35+40}\] and be done in one step

Answer 4

hmm I got 17 1/2 minutes, must have missed something

Answer 5

let me compute and see

Answer 6

did you compute
\[\frac{35\times 40}{35+40}\]

Answer 7

sox was close
it is actually
\[18\tfrac{2}{3}\]

Answer 8

my error, thanks :)

Answer 9

i cheated and used a calculator!