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Zorluk: ZorRatios, Rates, and Proportions

A team of 1010 workers, all working at the same constant rate, can complete a project in 1818 days. After working together for 66 days, additional workers are hired, all of whom work at the same rate as the original workers. If the remaining portion of the project is completed in 88 days, how many additional workers were hired?

Cevap: 5

Cevap

The correct answer is 5. Five additional workers were hired to complete the remaining work in 8 days.
The correct answer is 55. To find the number of additional workers hired, we first calculate the total work required for the project in worker-days. Since 1010 workers can complete the project in 1818 days, the total work is 10×18=18010 \times 18 = 180 worker-days. In the first 66 days, the 1010 workers complete 10×6=6010 \times 6 = 60 worker-days of work, leaving 180−60=120180 - 60 = 120 worker-days of work. To complete this remaining work in 88 days, the total number of workers required is 1208=15\frac{120}{8} = 15 workers. Subtracting the original 1010 workers gives 15−10=515 - 10 = 5 additional workers.

Adım Adım Çözüm

1
Calculate the total amount of work required for the project.
180180 worker-days
Since 1010 workers can complete the project in 1818 days, the total work is the product of the number of workers and the number of days: 10×18=18010 \times 18 = 180 worker-days.
2
Calculate the work completed in the first 66 days.
6060 worker-days
The original 1010 workers worked for 66 days, completing 10×6=6010 \times 6 = 60 worker-days of work.
3
Find the remaining work to be done.
120120 worker-days
Subtracting the completed work from the total work gives the remaining work: 180−60=120180 - 60 = 120 worker-days.
4
Find the total number of workers required to finish the remaining work in 88 days.
1515 workers
Dividing the remaining work of 120120 worker-days by the target time of 88 days gives the total number of workers needed: 1208=15\frac{120}{8} = 15 workers.
5
Calculate the number of additional workers hired.
55 workers
Subtract the original 1010 workers from the total 1515 workers required for the second phase: 15−10=515 - 10 = 5.

Anahtar Kavram

Inverse variation and rate-time-work relationships, specifically using the concept of worker-days to solve multi-stage rate problems.
Tahmini Süre:2m 30s
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Ratios, Rates, and Proportions

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