Randy pushed a box up a hill. It turned over 15 times and then turned over 5 times as it rolled back down toward Randy. He pushed the box again, and it turned over 20 times before it rolled back 10times. Continue the pattern.
To continue the pattern, we need to analyze the given information. According to the question, when Randy pushes the box up the hill, it turns over a certain number of times, and when it rolls back down, it turns over a different number of times.
From the information provided, we can deduce the following pattern:
- The number of times the box turns over when pushed up the hill is decreasing by 10 each time. It started with 15, then 5, and subsequently decreasing by 10 (20, 10, 0, -10, -20, ...)
- The number of times the box turns over when it rolls back down is increasing by 5 each time. It started with 5, then 10, and subsequently increasing by 5 (15, 20, 25, 30, 35, ...)
To continue the pattern, we can follow these rules:
1. When Randy pushes the box up the hill, the number of turns decreases by 10 each time.
2. When the box rolls back down, the number of turns increases by 5 each time.
Let's apply these rules to continue the pattern:
Randy pushed the box again:
- It turned over 20 times before rolling back down.
- It rolled back 10 times.
Continuing the pattern:
Randy pushed the box:
- It turns over 10 times.
- It rolls back 15 times.
Randy pushed the box:
- It turns over 0 times.
- It rolls back 20 times.
Randy pushed the box:
- It turns over -10 times.
- It rolls back 25 times.
Randy pushed the box:
- It turns over -20 times.
- It rolls back 30 times.
And so on.
Please note that the negative numbers represent the box's rotation direction. It's a way to indicate that the box is turning in the opposite direction (clockwise) when rolling back.