Question

Два мастера, работая вместе, могут выполнить заказ за 6 часов.Если первый мастер будет работать 9часов, а потом его сменит второй, то он закончит работу через 4 часа.За сколько времени может выполнить заказ каждый из местеров, работая отдельно.

Answer 1

х - скорость работы первого
у - скорость работы второго
1 - вся работа
тогда время = работа/скорость

1/(x+y)=6
9x+4y=1

x+y=1/6
9x+4y=1

x=1/6-y
3/2-9y+4y=1

x=1/6-y
5y=1/2

x=1/15 - скорость работы первого
y=1/10 - скорость работы второго

1/x=15 - время работы первого
1/y=10 - время работы второго.  

Answer 2

Calculation of Time for Each Master to Complete the Order

Let's solve the problem step by step.

We are given that two masters working together can complete the order in 6 hours. Let's assume that the rate at which they work together is 1 unit of work per hour.

Next, we are given that the first master works for 9 hours and then is replaced by the second master, who completes the remaining work in 4 hours.

To find out how much work each master does in one hour, we can set up the following equation:

9x + 4(1-x) = 6

Where: - x represents the fraction of work done by the first master in one hour. - (1-x) represents the fraction of work done by the second master in one hour.

Simplifying the equation, we get:

9x + 4 - 4x = 6

Combining like terms, we have:

5x = 2

Solving for x, we find:

x = 2/5

Therefore, the first master completes 2/5 of the work in one hour, and the second master completes 3/5 of the work in one hour.

To find out how much time each master would take to complete the order individually, we can set up the following equations:

For the first master: 9(2/5) = 18/5 hours

For the second master: 4(3/5) = 12/5 hours

Therefore, when working individually, the first master would take 18/5 hours to complete the order, and the second master would take 12/5 hours to complete the order.

Answer:

- The first master, working individually, would take 18/5 hours to complete the order. - The second master, working individually, would take 12/5 hours to complete the order.