The problem provided describes a scenario where a tortoise makes a journey in two parts, with two different modes of movement: walking at 4 m/s or crawling at 3 m/s. We are asked to find the lengths of the two parts of the journey based on different time combinations:

• When the tortoise walks the first part and crawls the second, it takes 110 seconds.
• When the tortoise crawls the first part and walks the second, it takes 100 seconds.

Let the lengths of the two parts of the journey be denoted as:

• $x$: length of the first part (in meters)
• $y$: length of the second part (in meters)

Scenario 1: Walk first, crawl second

• Time taken to walk the first part: $\frac{x}{4}$ seconds.
• Time taken to crawl the second part: $\frac{y}{3}$ seconds.

From the problem, the total time for this scenario is 110 seconds: $\frac{x}{4} + \frac{y}{3} = 110$

Scenario 2: Crawl first, walk second

• Time taken to crawl the first part: $\frac{x}{3}$ seconds.
• Time taken to walk the second part: $\frac{y}{4}$ seconds.

From the problem, the total time for this scenario is 100 seconds: $\frac{x}{3} + \frac{y}{4} = 100$

Now, let's solve this system of equations to find the values of $x$ and $y$.The solution to the system of equations gives the lengths of the two parts of the journey as:

• $x = 120 \, \text{m}$ (the length of the first part)
• $y = 240 \, \text{m}$ (the length of the second part)

Thus, the correct option is (c) 120 m, 240 m.

Do you have any questions or would you like more details on how this was solved?

Here are 5 related questions for further practice:

1. How would the times change if the walking speed increased to 5 m/s?
2. What if the tortoise took 150 seconds when walking first and 140 seconds when crawling first?
3. Can you express the total time as a function of walking and crawling speeds?
4. How would the result change if the second part of the journey was twice as long as the first part?
5. What is the total distance traveled by the tortoise?

Tip: When solving word problems, translating them into mathematical equations helps clarify the relationship between variables.