A dog chasing a rabbit, which has a start of 45m, jumps 3m every time the rabbit jumps 2m. In how many leaps does the dog overtake the rabbit?

45?

x= number of jumps taken.

3x = 45 + 2x
x=45

technically shouldnt it be 46 leaps since 45 leaps he will be tied with tthe dog

46

You're right! It would take the dog 46 leaps to overtake the rabbit. Thank you for pointing that out.

To calculate the number of leaps it takes for the dog to overtake the rabbit, we need to determine when the distances covered by the dog and rabbit are equal.

Let's break it down step by step:

1. First, we need to figure out how many jumps the rabbit has made when the dog starts chasing it.
- The rabbit jumps 2m every time, and the total distance covered by the rabbit is 45m.
- So, the number of jumps made by the rabbit is 45m / 2m = 22.5 jumps.

2. Next, let's calculate how far the dog jumps each time.
- The dog jumps 3m every time the rabbit jumps 2m.

3. Now, we can calculate the distance covered by the dog for each jump until it catches up with the rabbit.
- For every 2m the rabbit jumps, the dog jumps 3m.
- So, the dog jumps an extra 1m (3m - 2m) for every 2m the rabbit jumps.

4. Since the dog covers an extra 1m for every 2m the rabbit jumps, it will catch up with the rabbit after the same number of jumps.
- Therefore, the number of leaps it takes for the dog to overtake the rabbit is 22.5 jumps.

However, it is important to note that the number of leaps cannot be 22.5 since it is not a whole number. Therefore, the answer is not 45. Instead, we can say that it takes approximately 23 leaps for the dog to overtake the rabbit.