I've observed that the some work problems are solved using the formula AB/A+B(ex 6*7/6+7) while some are just added Example 1/6+1/7,, could any one tell me the difference and appropriate contexts to use the same,, THanks in advance.
A completes a work alone in 6 hrs and b in 7 hrs. In how many hrs do they complete the work together?
Rate of work of A = 1/6
Rate of work of B = 1/7
You add rates to get their combined rate = 1/6 + 1/7 = (6+7)/6*7
Time taken by them together is the inverse = 6*7/(6+7) (because Work = Rate * Time)
This is the formula you are talking about. We use it in this specific case - where we have individual time taken given and we need to find combined time taken.
When you just add (1/6+1/7), this is the combined rate, not the time taken together.
Alex, Bob, and Cathy are painters working for a new housing development project in which all the houses are exactly the same. Cathy can paint an entire house by herself in 8 hours; Bob, in 12 hours; and Alex, in 16 hours. What is the ratio of the time it takes Cathy to paint a house by herself to the time it would take Bob and Alex to paint a house, working together at their usual rate?
Time it would taken Alex and Bob to paint the house together = 12*16/(12+16) hrs
Time it takes Cathy to paint the house = 8 hrs
Required ratio = 8/12*16/28 = 7:6
Be wary of the formula. You can use it in only this situation. Say, if their rates are given instead of time or total work done is required etc, you cannot use it.
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