a worker has a new pump and an old pump. the new pump can fill a tank in five hours and the old pump can fill the same tank in 7 hours write and solve an equation for the time it will take both pumps to fill one tank if the pumps are used together.
rate of old pump = tank/7
rate of new pump = tank/5
combined rate = tank/7 + tank/5
= (5tank + 7tank)/35 = 12tank/35
combined time = tank/(12tank/35)
= 35/12
= 2 11/12 hours = 2hours and 55 minutes
2 Hours 55minutes
Let's assume that both pumps working together can fill the tank in 'x' hours.
To solve this problem, we can set up the following equation based on the rates of the pumps:
Rate of the new pump = 1 tank per 5 hours
Rate of the old pump = 1 tank per 7 hours
Rate when both pumps are used together = 1 tank per 'x' hours
Now, we can add up the rates of the new pump and the old pump to get the rate when they are used together:
(1/5) + (1/7) = 1/x
To solve this equation, we can find a common denominator and then combine the fractions:
(7/35) + (5/35) = 1/x
Simplifying further:
12/35 = 1/x
To isolate 'x', we can cross-multiply:
12x = 35
And to solve for 'x', divide both sides by 12:
x = 35/12
Therefore, it will take approximately 2.92 hours (or 2 hours and 55 minutes) for both pumps to fill one tank when used together.
To find the time it will take for both pumps to fill one tank when used together, we can use the concept of rates.
Let's denote the time it takes for both pumps to fill one tank as "t" hours.
First, let's determine the rate at which each pump fills the tank individually. The new pump can fill the tank in 5 hours, so its rate of filling is 1/5 of a tank per hour. Similarly, the old pump can fill the tank in 7 hours, so its rate of filling is 1/7 of a tank per hour.
Now, when both pumps are used together, their rates of filling are additive, since they are working simultaneously. Therefore, the combined rate of filling for both pumps is:
1/5 + 1/7 = (7 + 5) / (5 * 7) = 12 / 35
This means that when both pumps are used together, they fill 12/35 of a tank per hour.
To find the time it will take for both pumps to fill one tank, we can set up the equation:
(12/35) * t = 1
Multiplying both sides by 35/12, we get:
t = 35/12
Therefore, it will take both pumps approximately 2.92 hours (rounded to two decimal places) to fill one tank when they are used together.