The Student Room Group

Math problem

If Chris clean the house in 4 hours and Tom can clean the house 5 hours. How long does it take them to clean the hous as a team? Please answer in Hours, min and seconds. Show your work.
This is a classic question, that it might be helpful to just "remember how to do it".
(Yeah, I think this problem is worth spoiling. I still don't know how anyone expects a Year whatever student to have this line of logic without a worked example.)

"Chris can clean the house in 4 hours" is the same as "Chris can clean 1/4 of the house in 1 hour".
Same thing for Tom - i.e. Tom can clean 1/5 of the house in 1 hour.

Now, what proportion of the house can Chris and Tom clean in 1 hour? That would be 1/4+1/5.
Hopefully you can finish it off.

Now important note: #2 is a common error.
EDIT: now deleted, but the idea is Chris and Tom would take (4+5)/2 = 4.5 hours.

That would be saying if Chris and Tom both take 4 hours to clean the house, they will still take 4 hours to clean that one house if they work together - that doesn't really make sense in reality.
(edited 2 months ago)
Reply 2
The reciprocal button (1/x or x1x^{-1} )is much underused and inverts a unit from
(in this case) hours per house to houses per hour.

So Chris cleans at a rate of 414^{-1} ¼ houses per hour whilst tom cleans at a rate of 515^{-1} 1/5 house per hour.

Cleaning together they do ¼+1/5 of a house per hour so how do we convert [fraction found adding ¼+1/5] of a house per hour to hours per house? Take the reciprocal again to get a fraction giving hours per house.

This can be easily converted to hours minutes seconds using the , ,, button on a casio or, by hand,


subtract the whole number bit (which is your number of hours)


multiply by 60 to get minutes


subtract of the whole number bit (which is your minutes)


Multiply by 60 to get your seconds.


Frequent error 2.33 hours (for example) is NOT 2h 33 minutes

If you do everything on your calculator and don't round off, the answer is exact because a decimal may repeat but can be exact when converted to time. (Demonstrating the frequent limitations of decimal over systems based on other number such as 12 or 60).
(edited 2 months ago)

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