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?
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please help me
i have homeworks that in algebra, and those question i post are the questions i can't really solve
To solve this problem, let's break it down into steps:
Step 1: Understand the problem
A policeman is pursuing a snatcher. We are given that the snatcher is ahead by 72 leaps, and that the snatcher takes 6 leaps while the cop takes 5 leaps. Additionally, we are told that 4 leaps of the snatcher are equal in distance to 3 leaps of the cop. We need to determine how many leaps the cop will make before he catches the snatcher.
Step 2: Determine the distance covered by each person
Since we know that the snatcher takes 6 leaps while the cop takes 5 leaps, we can assume that the distance covered by the snatcher in 6 leaps is equal to the distance covered by the cop in 5 leaps.
Let's represent the length of one leap made by the cop as "x". Therefore, the length of one leap made by the snatcher would be (4/3)x, as 4 leaps of the snatcher are equal to 3 leaps of the cop.
Step 3: Represent the distance covered by each person
Let's assume that the distance covered by the cop before he catches the snatcher is "D". Therefore, the distance covered by the snatcher would be D + 72 (as the snatcher is ahead by 72 leaps).
Step 4: Equate the distances covered
Now we can set up an equation to represent the distances covered by each person:
5x (distance covered by the cop in 5 leaps) = (6 * (4/3)x) (distance covered by the snatcher in 6 leaps)
Step 5: Solve the equation
Let's solve the equation to find the value of "x":
5x = (6 * 4/3)x
5x = 8/3x
Dividing both sides by "x":
5 = 8/3
To make the equation true, we need to find the value of "x" that satisfies this equation. However, since the left-hand side (5) is not equal to the right-hand side (8/3), it means there is no solution for "x" that satisfies the equation.
Therefore, we cannot determine the number of leaps the cop will make before catching the snatcher based on the given information.