Question

One of the farms outside of town uses a water tank for irrigation. The water tank holds a total of 5600 gallons and the tank has three pipes through which water drains to irrigate three different areas of the field. When water is drained from the tank, pipe B drains twice as much water as pipe A. Pipe C drains 65 gallons more than pipe B. Assume the tank is drained completely before it is refilled, how many gallons of water does each pipe drain?

Answer 1

Hint: We first assume the amount of water pipe A drains. Then using the given condition we find out the amount of water each pipe drains. We add them to get the value of 5600. We solve the equation to find the value of the variable.

Complete step-by-step answer:
Let us assume the rate of irrigation from the pipes remains constant for the whole stretch.
The water tank holds a total of 5600 gallons. Pipe B drains twice as much water as pipe A. Pipe C drains 65 gallons more than pipe B.
Let us assume that pipe A drains $ x $ gallons of water. From the given condition of pipe B draining twice as much water as pipe A, we get that pipe A drains $ 2x $ gallons of water.
Similarly, as pipe C drains 65 gallons more than pipe B, we have that pipe C drains $ 2x+65 $ gallons of water.
As the tank is drained completely before it is refilled, the pipes empty the tank completely.
Therefore, the addition of the individual values of the pipes will give 5600.
 $ x+2x+2x+65=5600 $ .
The simplification gives $ 5x=5535 $ which gives $ x=\dfrac{5535}{5}=1107 $ .
The pipe A drains 1107 gallons. Pipe B drains $ 1287\times 2=2214 $ gallons. Pipe C drains $ 2574+65=2279 $ gallons.

Note: We need not to find the rate in which the pipe drains the water. The total amount of water drained is essential to find the solution. The problem is not about the time.