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Let's solve the problem step by step:

### Problem Statement:
Two conveyors working simultaneously can fill a container in 25 minutes, delivering a total of 875 kg of material. If one conveyor breaks down after 15 minutes, the other conveyor continues to operate alone for an additional 25 minutes to fill the container. We need to find the rates of delivery (in kg/min) of each conveyor.

### Solution:
Let:
- Rate of delivery of Conveyor A = \( a \) kg/min
- Rate of delivery of Conveyor B = \( b \) kg/min

When working together, they fill the container in 25 minutes:

1. **Total delivery working together**: 
   \[
   (a + b) \times 25 = 875 \quad \Rightarrow \quad 25a + 25b = 875
   \]
   Simplifying this equation:
   \[
   a + b = 35 \quad \text{(Equation 1)}
   \]

2. **After Conveyor B breaks down after 15 minutes:**
   - In the first 15 minutes, both conveyors are working:
     \[
     (a + b) \times 15 = 15a + 15b
     \]
   - The material delivered in the first 15 minutes:
     \[
     15(a + b) = 15 \times 35 = 525 \, \text{kg}
     \]
   - Remaining material to be delivered by Conveyor A alone:
     \[
     875 - 525 = 350 \, \text{kg}
     \]
   - Conveyor A continues alone for 25 minutes:
     \[
     25a = 350 \quad \Rightarrow \quad a = 14 \, \text{kg/min} \quad \text{(Equation 2)}
     \]

3. **Substituting the value of \( a \) in Equation 1**:
   \[
   14 + b = 35 \quad \Rightarrow \quad b = 21 \, \text{kg/min}
   \]

### Answer:
- Rate of delivery of Conveyor A: \( 14 \, \text{kg/min} \)
- Rate of delivery of Conveyor B: \( 21 \, \text{kg/min} \)

Would you like further details, or do you have any questions?

### Related Questions:
1. How would the problem change if Conveyor A broke down instead of Conveyor B?
2. What would be the effect on delivery time if both conveyors worked at the same rate?
3. How can you verify the rates of delivery are correct?
4. What if the combined rate of delivery was different; how would you adjust your calculations?
5. How would you calculate the total work done by each conveyor?

### Tip:
When solving problems involving rates and times, setting up clear equations that represent the scenario step-by-step can help you easily find the solution.

When working simultaneously, two conveyors fill a certain container in 25 minutes, delivering 875 kg of material. If one of the conveyors breaks down after 15 minutes, the other conveyor must continue delivering for a further 25 minutes in order to fill the container. Find the rates of delivery of each of the two conveyors.

This problem involves finding the rates of delivery for two conveyors that fill a container in 25 minutes. After one breaks down, the other must continue delivering. Explore the step-by-step solution and understand how to set up and solve this rate problem. Suitable for students in Grades 10-12.

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