Expert: Scott A Wilson - 10/11/2010

Question
Janet can shovel snow from her driveway in 30 minutes. Bill can do the same job in 55 minutes. How long would it take Janet and Bill to shovel the driveway if they worked together?

I have some similar problems to this that I understand, but they are done in hours or days, not minutes, so I'm not sure if the formula would be the same or if I have to do something else to the fractions before solving it.
In all the other problems, it is said that you put 1 over the number. For instance, if it takes a person 6 hours, then it would take them 1/6 of the time. So, would this be 1/30+1/55 and then put x*30+x/55=1 hour?

Answer
If the driveway is thought of a 1 unit, each minute Janet does 1/30 of the driveway and Bill does 1/55 if the driveway.

If n minutes are taken, the amount cleaned is 1/30 + 1/55.
This is the same as 11/330 + 5/330 = 16/330.

To complete the entire driveway, we would need n minutes where
16n/330 = 1.  This means that n = 330/16, which is a little more than around 20 minutes.

This is basically that same thing you said in x/30 + x/55 = 1,
but the 1 is in units of yard, not hour.


In converting it to hours, Janet cleans her driveway in 0.5 hours and Bill does the driveway in 11/12 of an hour.

If it took A 2 days and B 5 days, it would still be the same way.
That is, A does 1/2 in a day and B does 1/5 in a day.
Working together is 1/2 + 1/5 = 7/10 in a day.  This means that working together, it would only take 10/7 = 1 3/7 of a day.