Q work crew has two pumps, one new and one old. The new pump can fill a tank in 5 hours. The ols pump can fill the same tank in 7 hours.
a. How much of a tank can be filled in 1 hour with the new pump? with the old pump?
b.Write an expression for the number of tanks the new pump can fill in
(t) hours.
c. Write an expression for the number of tanks the old pump can fill in (t) hours.
d. Write and solve an equation for the time it will take th epumps to fill one tank if the pumps are used together.
rate of new pump = 1/5 tanks/hr
rate of old pump = 1/7 tanks/h
combined rate = 1/5 + 1/7 tanks/hr
= 12/35 tanks/hr
time to fill 1 tank with both pumps = 1 tank/(12/35) tanks/hr
= 35/12 hours
= 2 hours and 55 minutes
a. To find out how much of the tank can be filled in 1 hour with the new pump, we need to calculate the inverse of the time taken by the new pump to fill the tank. So, the new pump can fill 1/5th or 0.2 of the tank in 1 hour.
Similarly, the old pump can fill 1/7th or approximately 0.1429 of the tank in 1 hour.
b. The expression for the number of tanks the new pump can fill in (t) hours is given by:
(number of tanks) = t * (fill rate of new pump)
= t * (1/5)
= t/5
c. The expression for the number of tanks the old pump can fill in (t) hours is given by:
(number of tanks) = t * (fill rate of old pump)
= t * (1/7)
= t/7
d. When both pumps work together, their fill rates add up. So, the equation for the time it will take for the pumps to fill one tank is:
(t/5) + (t/7) = 1
To solve this equation, we can find the common denominator:
(7t + 5t) / 35 = 1
12t / 35 = 1
Cross-multiplying:
12t = 35
t = 35/12
t ≈ 2.92 hours
Therefore, it will take approximately 2.92 hours for the pumps to fill one tank if they are used together.
a. To find out how much of a tank can be filled in 1 hour with the new pump, we can use the concept of rates. The new pump fills a tank in 5 hours, so in 1 hour it can fill 1/5th of the tank.
b. To write an expression for the number of tanks the new pump can fill in (t) hours, we need to multiply the rate at which it fills the tank in 1 hour by the number of hours (t). Therefore, the expression would be (1/5) * t.
c. Similarly, for the old pump, since it fills the same tank in 7 hours, it can fill 1/7th of the tank in 1 hour. So the expression for the number of tanks the old pump can fill in (t) hours would be (1/7) * t.
d. To write and solve an equation for the time it will take for both pumps to fill one tank, we will consider their combined rate. Since they are working together, their rates will add up. The combined rate is 1 tank/hour. Let's denote the time it takes for both pumps to fill one tank as (T). Therefore, the equation would be (1/5 + 1/7) * T = 1.
To solve this equation, we can simplify the left side by finding a common denominator, which is 35. It becomes (7/35 + 5/35) * T = 1.
This simplifies to (12/35) * T = 1. To isolate T, we can multiply both sides by the reciprocal of (12/35), which is 35/12.
It becomes T = (35/12) * 1. Solving the right side gives T = 35/12, which is approximately 2.92.
Therefore, it will take the pumps approximately 2.92 hours to fill one tank if they are used together.