Time taken to boil same amount of water when both heaters are used in parallel:

To determine the time taken to boil the same amount of water when both heaters are used in parallel, we need to consider the rate at which each heater boils the water.

Let's assume that the first heater boils 1 unit of water in 15 minutes, and the second heater boils the same amount of water in 10 minutes. The boiling rate can be calculated as follows:

- Boiling rate of the first heater: 1 unit / 15 minutes = 1/15 units per minute
- Boiling rate of the second heater: 1 unit / 10 minutes = 1/10 units per minute

When both heaters are used in parallel, their boiling rates are added together. Therefore, the combined boiling rate can be calculated as:

Combined boiling rate = Boiling rate of the first heater + Boiling rate of the second heater

Calculating the combined boiling rate:
- Boiling rate of the first heater = 1/15 units per minute
- Boiling rate of the second heater = 1/10 units per minute

Combined boiling rate = 1/15 + 1/10 = (2 + 3) / 30 = 5/30 = 1/6 units per minute

This means that when both heaters are used in parallel, they can boil 1/6 units of water in 1 minute.

Calculating the time taken to boil the same amount of water:
To determine the time taken to boil the same amount of water, we need to find the reciprocal of the combined boiling rate. The reciprocal of 1/6 units per minute is 6/1 minutes per unit.

Therefore, when both heaters are used in parallel, it will take 6 minutes to boil the same amount of water.

Summary:
When both heaters are used in parallel, they have a combined boiling rate of 1/6 units per minute. This means that they can boil the same amount of water in 6 minutes.

Introduction:

In this scenario, we have two heaters, one of which can boil a certain amount of water in 15 minutes, while the other can boil the same amount of water in 10 minutes. We need to determine the time it would take to boil the same amount of water when both heaters are used in parallel.

Understanding the problem:

To solve this problem, we need to consider the individual rates at which the two heaters boil water and how their combined rate would change when they are used together. The rate at which a heater boils water can be determined by the inverse of the time it takes to boil the water.

Rate of boiling water:

- Heater 1: Boils water in 15 minutes. Therefore, its rate of boiling water is 1/15 (1 unit of water boiled in 15 minutes).
- Heater 2: Boils water in 10 minutes. Therefore, its rate of boiling water is 1/10 (1 unit of water boiled in 10 minutes).

Parallel operation:

When both heaters are used in parallel, their rates of boiling water add up. So, the combined rate of boiling water when both heaters are used together is the sum of their individual rates.

Combined rate = Rate of Heater 1 + Rate of Heater 2
Combined rate = 1/15 + 1/10

Finding the common denominator:

To add the two rates, we need to find a common denominator. In this case, the common denominator is 30.

Combined rate = (1/15) * (2/2) + (1/10) * (3/3)
Combined rate = 2/30 + 3/30
Combined rate = 5/30

Calculating the time:

To find the time taken to boil the same amount of water when both heaters are used in parallel, we can use the formula:

Time = Amount of water / Combined rate

Let's assume the amount of water to be boiled is 1 unit.

Time = 1 / (5/30)
Time = 30/5
Time = 6 minutes

Conclusion:

When both heaters are used in parallel, it would take approximately 6 minutes to boil the same amount of water. This is because the combined rate of boiling water is the sum of the individual rates of the heaters.