Write an equation of the line passing through (- 5,4) and having slope -7.
1 answer:
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Answer:
Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.
Step-by-step explanation:
Let tap B fills the pool alone in the time = x hours
So in one hour part of pool will be filled =
Another tap A when turned on, it takes time to fill the pool = x-5 hours
So in one hour part of the same pool filled =
Now both the taps A and B are turned on then time taken to fill the pool = 3 hours.
Part of the pool filled in one hour by both the taps =
Now we form an equation
Part of pool filled in one hour by tap A + Part of pool filled in one hour by tap B = Part of pool filled in one hour by both the taps when turned on
3(x - 4) = x(x - 5)
x² -5x = 3x - 12
x² - 8x + 12 = 0
x² - 6x - 2x + 12 = 0
x(x - 6) - 2(x - 6) = 0
(x -2)(x - 6) = 0
x = 2, 6 hours
We will take higher value of x as x = 6 hours for tap B.
Time taken by tap A = 6 - 4 = 2 hours.
Therefore, Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.
Adding: When adding fractions, you want to make sure that the denominator is the same for both fractions. If they are already the same, just add both the numerators to get the answer. For example,
If the denominator is different in both fractions, you have to find the least common denominator, or LCD. The LCD is the smallest number that both denominators can multiply into. For example, say you need to find
Multiply both the numerator and the denominator of (1/3) by 2 to get (2/6). This way, the denominators are the same and you can find the answer.
In the case that one denominator does not go into the other, find the smallest number they both multiply into. For example,
Here, the smallest number that both 4 and 3 multiply into is 12. Multiply both fractions by the correct amount to make both denominators 12. It would then become
Subtraction: follow the same rules as addition, except subtract the numerators instead of adding them.
Multiplication: multiply both numerators and both denominators.
Division: Flip one of the fractions and multiply.
Becomes
Hope this explains it all. Let me know if you have any questions :)
If the denominator is different in both fractions, you have to find the least common denominator, or LCD. The LCD is the smallest number that both denominators can multiply into. For example, say you need to find
Multiply both the numerator and the denominator of (1/3) by 2 to get (2/6). This way, the denominators are the same and you can find the answer.
In the case that one denominator does not go into the other, find the smallest number they both multiply into. For example,
Here, the smallest number that both 4 and 3 multiply into is 12. Multiply both fractions by the correct amount to make both denominators 12. It would then become
Subtraction: follow the same rules as addition, except subtract the numerators instead of adding them.
Multiplication: multiply both numerators and both denominators.
Division: Flip one of the fractions and multiply.
Becomes
Hope this explains it all. Let me know if you have any questions :)