3 gears are connected so that the two turns of the first wheel turn ii wheel nine times and the three terms of ii wheel turn the third wheel 5 times.
A. If you turn the first wheel once, how many times does the third wheel turn?
B. How many times must you turn the first wheel so that the third wheel turns 30 times?
The turns are in the ratios 2:9 and 3:5=9:15
So, they are in the ratios 2:9:15
Now things are clearer, right?
No I'm still confused how to answer A and B
To solve this problem, let's break down the information we have step by step.
First, we know that if you turn the first wheel once, it causes the second wheel to turn nine times. This tells us that the ratio of the first wheel's turns to the second wheel's turns is 1:9.
Next, we know that the three turns of the second wheel cause the third wheel to turn five times. This gives us a ratio of 3:5 between the second wheel and the third wheel.
Let's now use these ratios to answer the given questions:
A. If you turn the first wheel once, we determined that it will cause the second wheel to turn nine times. Since the ratio between the second wheel and the third wheel is 3:5, we can calculate the number of turns the third wheel will make.
First, we multiply the number of turns of the second wheel (9) by the numerator of the ratio between the second and third wheel (3):
9 * 3 = 27
Then, we divide this number by the denominator of the ratio between the second and third wheel (5):
27 / 5 = 5 remainder 2
Therefore, if you turn the first wheel once, the third wheel will turn 5 times with a remainder of 2.
B. To find out how many times you need to turn the first wheel for the third wheel to turn 30 times, we'll need to use the ratios once again.
Since the first wheel turns the second wheel nine times, and the ratio between the second and third wheel is 3:5, we can calculate the number of turns of the third wheel.
First, we multiply the desired number of turns for the third wheel (30) by the denominator of the ratio between the second and third wheel (5):
30 * 5 = 150
Then, we divide this number by the numerator of the ratio between the second and third wheel (3):
150 / 3 = 50
Therefore, you would need to turn the first wheel 50 times for the third wheel to turn 30 times.
Remember, the key to solving this problem is understanding the ratios between the gears and applying simple multiplication and division operations.