Three pumps filling up a tank &quot;A large tank can be filled by 2 similar small pumps and 1 larger pump working together in 1 hour and 12 minutes. The larger pump takes one hour less than the smaller pump to fill up the tank alone. Find how long each pump takes, given that V/P = T where V = volume of the tank, P = Pump, T = Time.&quot;
These are the exact words from a mathematics exam question and I'm unsure how to interpret P (I assumed it was the rate). If someone could provide a solution, that would be great.
This reminds me of the painting a room word problem. Let's proceed as follows.
Suppose the large pump can fill the tank in $t_L$ hours working alone, and the small pump can fill the tank in $t_S$ hours working alone.
Then $t_L=t_S-1$ and $\frac{1}{t_S}+\frac{1}{t_S}+\frac{1}{t_L}=\frac{1}{1.2}$. Combining these equations and simplifying yields $\frac{2}{t_S}+\frac{1}{t_S-1}=\frac{1}{1.2}$ This implies $t_S=4$ and $t_L=3$. (Note: $t_S=3/5$ is extraneous).
This reminds me of the painting a room word problem. Let's proceed as follows.
Suppose the large pump can fill the tank in $t_L$ hours working alone, and the small pump can fill the tank in $t_S$ hours working alone.
Then $t_L=t_S-1$ and $\frac{1}{t_S}+\frac{1}{t_S}+\frac{1}{t_L}=\frac{1}{1.2}$. Combining these equations and simplifying yields $\frac{2}{t_S}+\frac{1}{t_S-1}=\frac{1}{1.2}$ This implies $t_S=4$ and $t_L=3$. (Note: $t_S=3/5$ is extraneous).