A child can do a piece of work 15 hours slower than a woman. The child works for 18 hours on the job and then the woman takes charge for 6 hours. In this way, 3/5 of the work is completed. To complete the job now, how much time does the woman take?

Let the woman finish the whole work in W hours. Then the child finishes it in W + 15 hours. Work done: Child’s 18 hours work = 18 / (W + 15) Woman’s 6 hours work = 6 / W Total = 3/5 So, 18/(W+15) + 6/W = 3/5 Solve: Multiply by 5W(W+15): 5W·18 + 5(W+15)·6 = 3W(W+15) 90W + 30W + 450 = 3W² + 45W 120W + 450 = 3W² + 45W 3W² - 75W - 450 = 0 Divide by 3: W² - 25W - 150 = 0 Solve quadratic: W = [25 ± √(625 + 600)] / 2 W = [25 ± √1225] / 2 W = (25 ± 35) / 2 Positive solution → W = (25 + 35)/2 = 30 hours