The heights of three towers are in the ratio 5:6:7. If a spider takes 15 minutes to climb the smallest tower, how much time will it take to climb the highest one?

Options

A. 15 minutes
B. 18 minutes
C. 21 minutes
D. 54 minutes

Explanation

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Ratios
The heights of the three towers are given in the ratio 5:6:7. This means that if we let the height of the smallest tower be \(5x\), the second tower will be \(6x\), and the tallest tower will be \(7x\), where \(x\) is a common factor.

**Hint:** Ratios represent a relationship between quantities. Here, we can express the heights in terms of a variable \(x\).

### Step 2: Determine the Height of the Smallest Tower
Let’s denote the height of the smallest tower as \(5x\). The spider takes 15 minutes to climb this tower.

**Hint:** The time taken to climb is directly proportional to the height of the tower.

### Step 3: Calculate the Climbing Rate of the Spider
Since the spider takes 15 minutes to climb the smallest tower (height \(5x\)), we can find the climbing rate of the spider:
- Climbing rate = Height of smallest tower / Time taken = \(5x / 15\) = \(x / 3\) (units of height per minute).

**Hint:** The climbing rate helps us understand how much height the spider can cover in a minute.

### Step 4: Calculate the Time to Climb the Tallest Tower
Now, we need to find out how long it will take the spider to climb the tallest tower, which has a height of \(7x\).
- Time taken to climb the tallest tower = Height of tallest tower / Climbing rate = \(7x / (x / 3)\).

**Hint:** When calculating time, remember to divide the height by the climbing rate.

### Step 5: Simplify the Expression
Now, simplify the expression:
- Time taken = \(7x \times (3 / x)\) = \(21\) minutes.

**Hint:** When \(x\) cancels out, you are left with a numerical answer.

### Conclusion
The spider will take **21 minutes** to climb the tallest tower.

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