Question

Два рабочих,работая одновременно,обработали участок земли за 63 часа.За какое время смог бы обработать этот участок наиболее медленный рабочие,работая самостоятельно,если скорости выполнения работы этими рабочими относятся как 3:7?

Answer 1

1/х+1/у=1/63
3х=7у

63х+63у=ху
3х-7у=0          ( *9)

63х+63у=ху
27х-63у=0

90х=ху
3х=7у

у=90
3х=630

у=90(ч) - потребуется быстрому
х=210(ч) - потребуется медленному рабочему

Answer 2

Problem Analysis

We are given that two workers, working simultaneously, were able to complete a piece of land in 63 hours. We need to determine how long it would take the slowest worker to complete the same piece of land if they were working alone, given that the speeds of the workers are in a ratio of 3:7.

Solution

Let's assume that the faster worker completes the entire task in x hours. According to the given ratio, the slower worker would take 7x hours to complete the same task.

Since the two workers working together completed the task in 63 hours, we can set up the following equation:

1/x + 1/(7x) = 1/63

To solve this equation, we can find a common denominator and simplify:

(7 + 1)/7x = 1/63

8/7x = 1/63

Cross-multiplying, we get:

8 * 63 = 7x

504 = 7x

x = 504/7

x = 72

Therefore, the faster worker would complete the task in 72 hours, and the slower worker would take 7 times longer, which is 7 * 72 = 504 hours.

Answer

The slowest worker, working alone, would take 504 hours to complete the same piece of land.

Verification

Let's verify our answer using the given ratio of 3:7.

If the faster worker takes 72 hours to complete the task, the slower worker would take 7 times longer, which is 7 * 72 = 504 hours. This confirms that our answer is correct.