Problem Solving

In anticipation of a flood, a city engineer estimated that it would take 15 hours for a crew of 40 workers to build a dike 20 meters long around one of the city's wells. Using the same estimate of worker-hours per meter of dike, how many workers would be needed to build a similar dike 25 meters long around another well, if the dike needs to be completed in 6 hours?

A. 56
B. 60
C. 80
D. 100
E. 125

I think you can pretty easily knock out a couple of answers. A 20m dike takes 15 hours to complete when 40 workers are building it, and we need a longer dike in less than HALF the time. If we're going to cut time by over 50%, we need to increase rate by over 100% to make up for it, and the only way we can increase the rate of building is by adding more workers. We can eliminate A, B, and C.

We need 15*40 = 600 worker-hours to complete 20m. 25m is 25% greater than 20m, so we'll need 25% more worker hours to complete the new project. 1.25 * 600 = 750. Divide 750 worker-hours by 6 actual hours to see that we need 125 workers to complete the dike.

ritumaheshwari02 wrote:In anticipation of a flood, a city engineer estimated that it would take 15 hours for a crew of 40 workers to build a dike 20 meters long around one of the city's wells. Using the same estimate of worker-hours per meter of dike, how many workers would be needed to build a similar dike 25 meters long around another well, if the dike needs to be completed in 6 hours?

A. 56
B. 60
C. 80
D. 100
E. 125

Let the rate for each worker = 1 unit per hour.
Rate for 40 workers = 40 units per hour.
In 15 hours, the amount of work produced = 40*15 = 600 units.
Thus, the 20-meter dike is equal to 600 units of work.

To determine the number of units that need to be produced in order to build a 25-meter dike, set up a proportion:
20 meters/600 units = 25 meters/x units
1/30 = 25/x
x = 750 units.

To produce 750 units in 6 hours, the required rate = 750/6 = 125 units per hour.
Since each worker produces 1 unit per hour, the number of workers required = 125.

The correct answer is E.