SOLUTION: A and B make widgets. A and B together can finish making them in 24 days. A alone works for 16 days, then B alone works for 12 days. The rest of the widgets are 2/5 of the total. A

Question 1163804: A and B make widgets. A and B together can finish making them in 24 days. A alone works for 16 days, then B alone works for 12 days. The rest of the widgets are 2/5 of the total. A makes 3 more widgets than B per day. How many widgets need to be made in total?
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
A and B make widgets. A and B together can finish making them in 24 days.
A alone works for 16 days, then B alone works for 12 days.
The rest of the widgets are 2/5 of the total. A makes 3 more widgets than B
per day. How many widgets need to be made in total?

Let the total number of widgets that need be made = n. Let B's rate be x widgets/day. Then A' rate is x + 3 widgets per day. So in 24 days, B makes 24x widgets. And in 24 days, A makes 24(x + 3) widgets. In 24 days, together they make n widgets. When they work alone, A makes 16(x+3) widgets B makes 12x widgets Since the rest are 2/5 of n, working alone they made 3/5 of n Solve that for x and n. You finish. The required answer will be the value of n. Edwin

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Let x be the number of widgets produced each day by B; then the number produced by A each day is x+3.

A and B together can do the whole job in 24 days.

A working 16 days, and B working 12 days, can do 3/5 of the job (because 2/5 of the job remains to be done).

B produces 6 widgets a day; A produces 9.

Together in a day they produce 15 widgets.

Together they complete the job in 24 days, so the number of widgets is 24*15 = 360.

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