A team of street pavers was assigned the task of paving two parking lots one twice the size of the other. They worked for the first half of the day on the larger parking lot. Then the team split into two groups of equal number. The first group continued working on the larger parking lot and finished it by evening. The second group paved the smaller parking lot, but did not finish by evening. The next day one street-paver finished the smaller parking lot in a single day's work. How many street-pavers were on the original team?

Question

A team of street pavers was assigned the task of paving two parking lots one twice the size of the other. They worked for the first half of the day on the larger parking lot. Then the team split into two groups of equal number. The first group continued working on the larger parking lot and finished it by evening. The second group paved the smaller parking lot, but did not finish by evening. The next day one street-paver finished the smaller parking lot in a single day's work. How many street-pavers were on the original team?

Answer 1

Since they had to have finished over half of the parking lot by midday and the rest was finished by the end of the day with half the people they must have finished ⅔. And since the other half of the team was working on the smaller pavement ⅔ of the pavement got done since that is the equivalence of ⅓ of the larger pavement. Since 1 person did ⅓ of the smaller lot in one day then 2 people can finish ⅓ in half a day meaning that 4 people worked on the smaller pavement the second half of the day.

This means that the original team had 8 workers

Answer 2

To solve this problem, let's work through the information step by step.

We are given that the team of street pavers was assigned the task of paving two parking lots. One parking lot is twice the size of the other.

Let's say the smaller parking lot takes 'x' hours to be paved by one street paver, and the larger parking lot takes '2x' hours to be paved by one street paver. Remember that the larger parking lot is twice the size of the smaller one.

Now, let's consider the first half of the day when the entire team worked on the larger parking lot. Since we don't know the number of street pavers in the team, let's represent it as 'n'. Thus, the work done in the first half of the day is 'n * 2x' (since each street paver takes '2x' hours to pave the larger lot).

After the first half of the day, the team split into two equal groups. Therefore, each group has 'n/2' street pavers.

The first group continued working on the larger parking lot and finished it by evening. Since the work done by the entire team in the first half of the day is 'n * 2x', and this work was done by 'n/2' street pavers for the remaining half, the total work done on the larger parking lot is '(n * 2x) * (n/2)'.

The second group paved the smaller parking lot but did not finish it by evening. Since one street paver finishes the smaller parking lot in a single day's work, the work done by the second group is 'x * (n/2)'.

Given that the work done on the larger parking lot is equal to the work done on the smaller parking lot, we have the equation:

'(n * 2x) * (n/2) = x * (n/2)'

Simplifying this equation, we get:

'n^2 * 2x = x * (n/2)'

Now, let's eliminate the common factors of 'x' and '(n/2)' from both sides:

'2n^2 = 1'

Dividing both sides by 2:

'n^2 = 1/2'

Taking the square root of both sides:

'n = sqrt(1/2)'

Simplifying this expression, we have:

'n = 1/sqrt(2)'

To find the number of street pavers on the original team, we need to solve for 'n'. However, the square root of 1/2 is a fraction, which means the value of 'n' is not an integer. Since the question asks for the number of street pavers, it is not possible to determine an exact answer with the given information.

Therefore, we cannot determine the number of street pavers on the original team based on the information provided.