Question

May you please help me..

1. Charlie can construct 100 identical boxes in two days less than Cholo. If they work together they can finish the work in 5 5/6 days. How long will it take each of them to finish 100 boxes?
2. It takes Peter 6 hours longer than Luis to do a certain job. Together they can do it in 4 hours. How long would it take each working alone to do the job?

Answer 1

Let r be the number of boxes Charlie makes per day. Let t be the number of days it takes him to make 100 boxes. r * t = 100 and r = 100/t

Cholo makes 100 boxes in t + 2 days. For Cholo, the rate is 100/(t+2) boxes per day

Now we know that both Cholo and Charlie working together produce
\[\frac{100}{t} + \frac{100}{t+2}\] boxes per day. We also know that they can produce 100 boxes in 5 5/6 days if they work together.

\[100 = (\frac{100}{t} + \frac{100}{t+2}) * 5\frac{5}{6}\]

Solve for t to get the number of days it will take Charlie to make 100 boxes. Add 2 to t to get the number of days it will take Cholo to make 100 boxes.

For the second problem, let P be the number of hours Peter takes, and L be the number Luis takes. P = 6 + L.

Figure this one in terms of a fraction of the job completed. In 1 hour, Peter has done 1/P of the work, and in 1 hour, Luis has done 1/L of the work. Working together, they complete the job in 4 hours. Again, we combine their rates and solve:

complete job = 1 = rate * time
\[1 = (\frac{1}{P} + \frac{1}{L})*4 = (\frac{1}{L+6}+\frac{1}{L})*4\]Solve for L, then use that to find P.