Two typists of different speeds can complete a typing job together in 6 minutes. If the 1st typist types alone for 4 minutes and then the 2nd typist types alone for 6 minutes, they would be left with 1/4 of the total work. In how many minutes can the slower typist complete the job working alone?

Solution

ATQ, Let the 1st typist take x minutes and the 2nd typist take y minutes to complete the work alone. Then, 1/x + 1/y = 1/6 ---- (i) When 1st types 4 minutes and 2nd types 6 minutes, work done = 3/4, so 4/x + 6/y = 3/4 ---- (ii) From (i), 1/x = 1/6 − 1/y Substitute in (ii): 4(1/6 − 1/y) + 6/y = 3/4 4/6 − 4/y + 6/y = 3/4 2/3 + 2/y = 3/4 2/y = 3/4 − 2/3 2/y = (9 − 8)/12 = 1/12 y = 24 From (i), 1/x + 1/24 = 1/6 1/x = 1/6 − 1/24 = 4/24 − 1/24 = 3/24 = 1/8 x = 8 Slower typist takes = 24 minutes.