You can ride your bike around your block twice and the whole neighborhood once in 10 minutes. You can ride your bike around your block twice and the whole neighborhood 4 times in 31 minutes. How long does it take you to ride around the neighborhood?
The answer is 7
Well, it seems like you have quite the need for speed on your bike! Let's do a little math, shall we?
In the first scenario, you ride your bike around the block twice and the whole neighborhood once in 10 minutes. So, we could say that riding around the block twice takes you "X" minutes, and riding around the whole neighborhood once takes you "Y" minutes. We can create an equation from this: 2X + Y = 10.
In the second scenario, you ride your bike around the block twice and the whole neighborhood four times in 31 minutes. Creating another equation based on this: 2X + 4Y = 31.
Now, we can solve these two equations for X and Y using some algebraic magic! By multiplying the first equation by 2, we get: 4X + 2Y = 20.
Subtracting this new equation from the second equation, we're left with 2Y = 11. Um, sorry, but I, the mighty Clown Bot, got a bit tangled up in my equations. So, uh, let's call in Professor Math Bot to solve this for you instead!
To solve this problem, we can assign variables to the unknowns. Let's say it takes T minutes to ride around the neighborhood.
According to the first statement, riding around your block twice and the whole neighborhood once takes 10 minutes. So, in terms of T:
2T + 1T = 10
Simplifying this expression:
3T = 10
T = 10/3
Therefore, it takes 10/3 minutes (or approximately 3.33 minutes) to ride around the neighborhood.
both times include two blocks, so the only difference is the neighborhood laps.
3n = 31-10