Let's solve the problem step by step.

Step 1: Calculate the charging rate of one large solar panel.

We know that 2 large solar panels charge the electric car in 240 minutes. Therefore, the charging rate of 2 large solar panels is:

$\text{Rate of 2 large panels} = \frac{1 \text{ car}}{240 \text{ minutes}}$

The charging rate of one large solar panel is half of this:

$\text{Rate of 1 large panel} = \frac{1}{2} \times \frac{1 \text{ car}}{240 \text{ minutes}} = \frac{1}{480} \text{ cars per minute}$

Step 2: Calculate the charging rate of one small solar panel.

It’s given that 2 large panels charge the car in the same time as 6 small panels. Therefore, 6 small solar panels also charge the car in 240 minutes.

The charging rate of 6 small panels is:

$\text{Rate of 6 small panels} = \frac{1 \text{ car}}{240 \text{ minutes}}$

The charging rate of one small panel is:

$\text{Rate of 1 small panel} = \frac{1}{6} \times \frac{1 \text{ car}}{240 \text{ minutes}} = \frac{1}{1440} \text{ cars per minute}$

Step 3: Calculate the total charging rate of 5 large panels and 3 small panels.

Now, we need to find the combined charging rate of 5 large panels and 3 small panels.

• The charging rate of 5 large panels is:

$\text{Rate of 5 large panels} = 5 \times \frac{1}{480} = \frac{5}{480} = \frac{1}{96} \text{ cars per minute}$

• The charging rate of 3 small panels is:

$\text{Rate of 3 small panels} = 3 \times \frac{1}{1440} = \frac{3}{1440} = \frac{1}{480} \text{ cars per minute}$

Step 4: Combine the rates.

The total charging rate of 5 large panels and 3 small panels is the sum of their individual rates:

$\text{Total rate} = \frac{1}{96} + \frac{1}{480}$

To add these fractions, we need a common denominator. The least common denominator of 96 and 480 is 480. Rewrite the fractions:

$\frac{1}{96} = \frac{5}{480}$

Now, add the fractions:

$\text{Total rate} = \frac{5}{480} + \frac{1}{480} = \frac{6}{480} = \frac{1}{80} \text{ cars per minute}$

Step 5: Calculate the time required.

If the total rate is $\frac{1}{80}$ cars per minute, this means the system of 5 large panels and 3 small panels charges $\frac{1}{80}$ of the car per minute. Therefore, to charge 1 whole car, the time required is:

$\text{Time} = \frac{1 \text{ car}}{\frac{1}{80} \text{ cars per minute}} = 80 \text{ minutes}$

Final Answer:

It will take 80 minutes for 5 large solar panels and 3 small solar panels to charge the car.

Would you like further details on any part of this solution?

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Here are 5 related questions to extend this concept:

1. How long would it take for 4 large solar panels to charge the car?
2. What would be the charging time if you only used 3 small solar panels?
3. If 8 small solar panels are used, how long would it take to fully charge the car?
4. What is the ratio of charging rates between large and small solar panels?
5. How many small solar panels are needed to charge the car in 240 minutes?

Tip: Always convert rates into their simplest form before summing them to make the calculations easier.