A 15-person road crew is scheduled to finish repairing a highway in 12 days. On the morning of the fifth day, several new workers join the crew and, together, they complete the remaining repairs in 6 days. How many new workers joined the crew?

15 * 12 = 180

so
The whole job requires 180 man days

They worked for 4 days
so did 15 * 4 = 60 man days

they have 120 man days of work left
120 / n = 6
n = 20 men on the job

so 5 new men joined

Let's break down the problem step by step:

Step 1: Calculate the work done by the original crew in the first 5 days.
Since the original crew consists of 15 people and they worked for 5 days, the work done by the original crew is given by:
Work done by original crew = (15 people) * (5 days)

Step 2: Calculate the remaining work that needs to be done.
Since the entire job can be completed in 12 days by the original crew, the remaining work after 5 days is given by:
Remaining work = (Total work) - (Work done by original crew)
Total work = (15 people) * (12 days)

Step 3: Calculate the work done by the new workers in the remaining 6 days.
According to the problem, the new workers, along with the original crew, completed the remaining work in 6 days. Let's assume "x" represents the number of new workers. Therefore, the work done by the new workers in 6 days is given by:
Work done by new workers = (15 people + x) * (6 days)

Step 4: Set up an equation using the work done by the original crew and the work done by the new workers.
Since the total work done by both the original crew and the new workers is equal to the remaining work, we can set up the following equation:
Work done by original crew + Work done by new workers = Remaining work

Step 5: Solve the equation to find the value of "x" (the number of new workers).
Using the equations from step 1, step 2, and step 3, we can substitute the values and solve for "x":
(15 people) * (5 days) + (15 people + x) * (6 days) = (15 people) * (12 days)

Step 6: Simplify and solve for "x".
(15 * 5) + (15 + x) * (6) = (15 * 12)
75 + 90 + 6x = 180
6x = 180 - (75 + 90)
6x = 180 - 165
6x = 15
x = 15 / 6
x = 2.5

Step 7 (Final Answer): Interpret the answer.
Since it is not possible to have a fraction of a worker, we can conclude that 2 new workers joined the crew.

Therefore, the number of new workers who joined the crew is 2.

To solve this problem, we can start by figuring out the rate at which the original 15-person road crew can repair the highway. Let's call this rate "R."

We know that the original 15-person road crew can complete the highway repair in 12 days. This means that the crew's combined work rate is 1/12 of the total job per day.

So, if R represents the rate of the original crew, then we have:
15R = 1/12 (since it takes them 12 days to complete the job)

Now, let's consider the situation on the morning of the fifth day when some new workers join the crew. We don't know the exact number of new workers, so let's call it "N."

The original crew worked for 5 days and completed a fraction of the job, while the new crew, consisting of the original 15 workers plus the N new workers, worked for 6 days and completed the remaining fraction of the job.

The total fraction of the job completed by both crews together is 1 (the whole job was completed).

For the original crew:
5 days * (15R) = fraction of the job completed

For the new crew:
6 days * (15 + N) * R = fraction of the job completed

Summing these two fractions together gives us the equation:
5(15R) + 6(15 + N)R = 1

Simplifying this equation, we get:
75R + 90R + 6NR = 1
165R + 6NR = 1

Now, we can solve for N, the number of new workers who joined the crew.

Since we know that R = 1/12 (from 15R = 1/12), we can substitute this value into the equation:
165(1/12) + 6N(1/12) = 1
165/12 + 6N/12 = 1
165 + 6N = 12
6N = 12 - 165
6N = -153
N = -153/6
N = -25.5

Since the number of new workers cannot be negative or non-integer, we can conclude that there were no new workers joining the crew.

no!!!! i didnt do it for free, they pay you money! jk the answer is 20/4, simplified is 5