Two masons laying bricks [closed]

Question

I'm having trouble solving a puzzle in Swedish. I've translated it to English:

Two masons work on a project. One mason can complete the project alone in 8 hours, while the other can complete it alone in 10 hours. When they work together, they can finish the project in 5 hours, but they lay 30 fewer bricks per hour.

The question is: how many bricks do they lay together?

I'm not sure where to start, and I'm having trouble figuring out how to approach this problem. I did come across a solution that suggests the answer is 1200 bricks. According to this solution, if the number of bricks is X, then the first mason lays 0.1X bricks per hour, the second mason lays 0.125X bricks per hour, and together they lay 0.2X bricks per hour.

The equation to solve is 0.1X+0.125X-30=0.2X (-30 for the 30 fewer bricks per hour). The solution to this equation is X=1200.

However, I'm not sure if this solution is correct, and I'm not sure how to approach this problem on my own.

Answer 1

The solution is either 2400 bricks or 1200 bricks, depending on how you interpret the clause

When they work together [...] they lay 30 fewer bricks per hour.

If you interpret that each one lays 30 fewer bricks per hour than their corresponding individual rate when working alone, then the solution is 2400 bricks. For the case when the combined rate is 30 fewer bricks per hour than the resulting rate of adding both original rates, then the solution is 1200 bricks.

Let N be the amount of bricks to complete the project.

a is the rate of the first mason:

a = N / 10h

b is the rate for the second mason:

b = N / 8h

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Case 1, each mason lays 30 fewer bricks per hour than their original rate

Let's define a' and b' as the rates of each mason when working together:

a' = a - 30bricks / 1h

a' = N / 10h - 30bricks / 1h

a' = (N - 300bricks) / 10h

similarly,

b' = (N - 240bricks) / 8h

Let c be the combined rate of both masons working together:

c = a' + b' = (N - 300bricks) / 10h + (N - 240bricks) / 8h =

c = (8N - 2400bricks + 10 N -2400bricks) / 80h

c = (18N - 4800bricks) / 80h

By definition, we are also given the value of the combined rate c:

c = N / 5h

Equating the right side of the last 2 expressions:

(18N - 4800bricks) / 80h = N / 5h

(18N - 4800bricks) / 80h = 16 N / 80h

getting rid of 1 / 80h at both sides:

18N - 4800bricks = 16 N

2N = 4800bricks

N = 2400 bricks

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Case 2, the combined rate of both masons is 30 fewer bricks per hour than the sum of their original rates

In this case, c as a function of a and b is defined as:

c = a + b - 30bricks / 1h

c = N / 10h + N / 8h - 30bricks / 1h

c = 8N / 80h + 10N / 80h - 2400bricks / 80h

c = (18N - 2400bricks) / 80h

again, equating to the given definition of c:

(18N - 2400bricks) / 80h = N / 5h

(18N - 2400bricks) / 80h = 16 N / 80h

getting rid of 1 / 80h at both sides:

18N - 2400bricks = 16 N

2N = 2400bricks

N = 1200 bricks