A group of women working together at the same rate can build a wall in 45 hours. When the work started, all the women did not start working together. They joined the work over a period of time, one by one, at equal intervals. Once at work, each one stayed till the work was complete. If the first woman worked 5 times as many hours as the last woman, for how many hours did the first woman work?

Step-by-step solution

Let n women complete the work in 45 hr . Then 1 woman can complete the work in 45 n hr . Each woman's work of 1 hr = 1 45 n . According to given question let each woman join the work after d hrs. of previous women started the work. Now, total work is finished in T hours after the work started by first woman. Time for which the first woman work =T hr . Time for which the n^ th women work = T-(n-1) d hr . A.T.Q : 5 T-(n-1) d =T aligned & 4 T 5 =(n-1) d & and T 45 n + T-d 45 n + T-2 d 45 n + + T-(n-1) d 45 n =1 & n T-