Question

If sue can shovel the driveway in 50 minutes and jim can do it in 60, how long would it take for both of them to do it together?

Answer 1

you wanna do it the real quick snap way?

Answer 2

using only the two numbers given to you, and no equation at all compute
\[\frac{50\times 60}{50+60}\]

Answer 3

i can explain why that is the right answer if you like, but that is all you really have to do here

Answer 4

Would you mind explaining for me please?

Answer 5

ok sure
but first is it clear what we are going to compute at the end of the explanation?

Answer 6

Sorta...

Answer 7

\[\frac{50\times 60}{50+60}=\frac{3000}{110}=\frac{300}{11}\] or your can write it as a mixed number \[27\tfrac{3}{11}\]

Answer 8

now that we see how easy it is, ready for the explanation?

Answer 9

Yes!

Answer 10

ok
sue can shovel the driveway in 50 minutes
that means her rate is \(\frac{1}{50}\) of the job per minute
jim can do it in 60 minutes
his rate is \(\frac{1}{60}\) of the job per minute

Answer 11

their combined rate is what you get when you add them and
\[\frac{1}{50}+\frac{1}{60}=\frac{50+60}{50\times 60}\]

Answer 12

i am not going to compute this number just leave it alone

Answer 13

then since that is their rate, \(\frac{50+ 60}{50\times 60}\) you want the time it takes to complete one job, in other words you want to solve
\[\frac{50+60}{50\times 60}T=1\] for \(T\) and you solve for \(T\) by multiplying by the reciprocal so
\[T=\frac{60\times 50}{50+60}\]

Answer 14

you do more than two of these you can go straight to the answer while all your colleagues are trying to write down some equation

Answer 15

Wow thank you so much I really appreciate the help!!!

Answer 16

yw

Answer 17

hope it is more or less clear

Answer 18

it was very clear,, better than how my teacher explained it

Answer 19

lol thanks!