Question

A company was hired to build a tunnel through a mountain. The company started at the south end of the mountain and completed only five hundred eighty five feet of the required seven thousand, six hundred five feet before going bankrupt. A different company was hired to complete the job, but th

ey decided to use two crews. Crew A would start where the other company left off at the southern end, while Crew B would start at the northern end and dig towards the other crew. Crew A was able to dig fifty eight feet of the tunnel per week. Crew B, which was larger, was able to dig fifty nine feet of the tunnel per week.

Answer 1

Let's denote crew A's work per week as A and crew B's work per week as B.

We are given that A = 58 ft per week and B = 59 ft per week.

We have to calculate how many weeks it will take both crews to complete the tunnel.

585 feet have already been dug from the south end. So, the total tunnel length that needs to be dug is 7605 - 585 = 7020.

Now, let's assume that both the crews continue to work at their respective rate of A = 58 ft/week and B = 59 ft/week.

Therefore, total tunnel length that needs to be dug in weeks = (7020 ft) / (A + B)

= (7020 ft) / (58 ft/week + 59 ft/week)

= 120.20 weeks

Hence, it will take a total of 120.20 weeks for both crews to complete the tunnel.