If Joe paints a house in 5 hours and Mike paints the same house in 3 hours then if they paint it together then how much will it take? If we do this question by 1/5 & 1/3 and then join each time piece together in order to reach 1 (as the house is 1) then the answer is approx. 1.87, now I found on google that there's a formula for such problem which is a+b/ab where a & b are 5 & 3, then still the answer is approx. 1.87, My question is that how we found this formula?
P.s. this question is from some Hollywood movie.

Question

If Joe paints a house in 5 hours and Mike paints the same house in 3 hours then if they paint it together then how much will it take? If we do this question by 1/5 & 1/3 and then join each time piece together in order to reach 1 (as the house is 1) then the answer is approx. 1.87, now I found on google that there's a formula for such problem which is a+b/ab where a & b are 5 & 3, then still the answer is approx. 1.87, My question is that how we found this formula?
P.s. this question is from some Hollywood movie.

anonymous · Answer

In 1 hour Joe will paint 1/5 of house

In 1 hour Mike will paint 1/3 of house
                                                             1           1
Together in 1 hour they will paint ---- + ----- of house
                                                             5            3

Now when we add the two fractions the LCD will be 5*3 = 15 (ab)
        1          1           3 + 5           b + a             a + b
so ---- + ---- = -------- = -------- or --------
        5          3             5*3              ab                  ab

anonymous · Answer

Good explanation harkirat!

anonymous · Answer

Sorry the formula is ab/a+b

anonymous · Answer

OK so the whole formula is 1 /(a+b/ab)