Answer:
Explanation:
To determine how long it will take to fill the air bed when both pumps A and B are used, we need to calculate their combined filling rate.
Pump A can fill up the air bed in 30 minutes, while Pump B can fill it up in 20 minutes. This means that Pump A fills at a rate of 1/30 of the bed per minute, and Pump B fills at a rate of 1/20 of the bed per minute.
To find the combined filling rate, we add the rates of Pump A and Pump B together. So, the combined rate is:
1/30 + 1/20
To simplify this expression, we need to find a common denominator. In this case, the least common multiple (LCM) of 30 and 20 is 60. Therefore, we can rewrite the expression with a common denominator:
2/60 + 3/60
Now that the denominators are the same, we can add the numerators:
2/60 + 3/60 = 5/60
So, the combined filling rate of Pump A and Pump B is 5/60 of the air bed per minute.
To determine how long it will take to fill the air bed completely, we need to calculate the reciprocal of the combined filling rate:
1 / (5/60)
To divide by a fraction, we multiply by its reciprocal:
1 * (60/5) = 60/5
Simplifying this expression, we get:
60/5 = 12
Therefore, it will take 12 minutes to fill the air bed completely when both Pump A and Pump B are used.