a policeman is pursuing a snatcher who is ahead by 72 of his own leaps. the snatcher takes 6 leaps while the cop takes 5 leaps, but 4 leaps of the snatcher are as long as 3 leaps of the cop. how many leaps will the cop make before he catches the snatcher?

Let's say the cop's leaps are 4 ft, while the snatcher's are 3 feet,

and the cop's leaps take 6 seconds, while the snatcher's take 5 seconds.

So, after x seconds, the distances and times must match up:

(x/6)(4) = (x/5)(3) + 72*3
x = 3240

So, it will take 3240/6 = 540 cop leaps to ctahc up.

Well, it sounds like the snatcher has really been leap-frogging ahead! But don't worry, I'll help the cop catch up in no time. Let's break it down.

We know that for every 5 leaps the cop takes, the snatcher takes 6 leaps. And for every 3 leaps of the cop, the snatcher takes 4 leaps.

So let's find out how many leaps the snatcher is ahead by using the ratios:

5 leaps (cop) vs 6 leaps (snatcher) = 72 leaps (the snatcher's lead)

Now, let's convert the snatcher's leaps to cop's leaps using the second ratio:

6 leaps (snatcher) to 4 leaps (cop) = ?? leaps (snatcher's lead)

If 6 leaps of the snatcher equal 4 leaps of the cop, we can find out how many leaps the snatcher's lead is in cop's leaps:

1 leap (snatcher) = (4/6) leaps (cop)
1 leap (snatcher) = (2/3) leaps (cop)

Now we can determine how many leaps the snatcher is ahead in terms of cop's leaps:

(2/3) leaps (cop) x 72 leaps (snatcher's lead) = 48 leaps (snatcher's lead in cop's leaps)

So, the snatcher is ahead by 48 leaps in terms of cop's leaps. But we want to know how many leaps the cop makes before catching the snatcher.

If the snatcher is ahead by 48 leaps and the cop takes 5 leaps for every 48 leaps the snatcher takes, we can divide the snatcher's lead by the cop's leaps:

48 leaps (snatcher's lead in cop's leaps) divided by 5 leaps (cop) = 9.6 leaps

Since we can't have fractional leaps, we'll round up to the nearest whole number. So the cop will make 10 leaps before catching the snatcher.

Get ready to cheer for the cop as he leaps into action!

Let's break down the information given step by step:

1. The snatcher is ahead by 72 of his own leaps.
2. The snatcher takes 6 leaps while the cop takes 5 leaps.
3. 4 leaps of the snatcher are equivalent to 3 leaps of the cop.

To find out how many leaps the cop needs to catch the snatcher, we can set up a proportion using the information in step 3:

4 snatcher leaps = 3 cop leaps

Now, let's proceed with the calculations:

1. Let's assume the number of cop leaps needed to catch the snatcher as 'x'.

2. The snatcher's number of leaps can be expressed as 'x + 72' since the snatcher is ahead by 72 leaps.

3. Using the proportion we set up earlier, we can set up an equation:

(x + 72) / 6 = x / 5

4. Solving for 'x':

5(x + 72) = 6x

5x + 360 = 6x

360 = 6x - 5x

360 = x

Therefore, the cop will need to make 360 leaps before he catches the snatcher.

To solve this problem, let's break it down step by step:

Step 1: Determine the distance covered by each leap of the cop and the snatcher.

Let's assume that each leap of the cop covers a distance of 'x' units, while each leap of the snatcher covers a distance of 'y' units.

We know that 4 leaps of the snatcher are as long as 3 leaps of the cop. Mathematically, we can express this as:

4y = 3x ---(Equation 1)

Step 2: Understand the given information.

We are given that the snatcher is ahead by 72 of his own leaps. This means that the snatcher's total distance covered is 72y units more than the cop's total distance covered.

Step 3: Set up an equation to represent the relative distances covered.

Let 'd' be the total number of leaps made by the cop before he catches the snatcher.

Thus, the cop's total distance covered can be expressed as 5dx, and the snatcher's total distance covered can be expressed as (4d + 72)y.

Step 4: Set up an equation to represent the relation between the distances covered.

Since the cop is pursuing the snatcher, the cop's total distance covered must be equal to or greater than the snatcher's total distance covered.

Therefore, we can set up the equation:

5dx ≥ (4d + 72)y ---(Equation 2)

Step 5: Substitute Equation 1 into Equation 2.

Substitute 4y from Equation 1 into Equation 2:

5dx ≥ (3x + 72)y

Step 6: Simplify the equation.

Divide both sides of the equation by xy:

5d ≥ 3x + 72

Step 7: Determine the possible values of 'd'.

Since 'd' represents the number of leaps made by the cop, it must be a positive integer.

To find the smallest value of 'd' that satisfies the inequality, we can start with 'd' equal to 1 and increment it until the inequality is satisfied.

For 'd' = 1:

5 ≥ 3x + 72

Solving for 'x', we get:

3x ≤ -67

This means that 'd = 1' doesn't satisfy the inequality.

For 'd' = 2:

10 ≥ 3x + 72

Solving for 'x', we get:

3x ≤ -62

Again, 'd = 2' doesn't satisfy the inequality.

We can continue this process and increment 'd' until we find the smallest positive integer value that satisfies the inequality.