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# [Smart Math] Algebra Problem 16

Here’s and example of a SMART MATH problem for ALGEBRA.

### Problem

It takes 60 turns for one vessel to empty the tank. How much turns would it take totally to empty the tank if the vessel is used alternately with another one 1/3rd its capacity?

1. 30
2. 90
3. 100
4. 60
5. 45

### The Usual Method

Let the vessels be A and B.

Vessel A takes 60 turns to empty the tank so vessel B will take 60 x 3 = 180 turns to empty the tank as it is only 1/3rd the size of the vessel A.

If both vessels work together $\frac{1}{60}$ of the tank will be emptied by vessel A and $\frac{1}{180}$ of it will be emptied by vessel B.

Hence, $\frac{1}{60}$ + $\frac{1}{180}$ of the tank will be emptied by one turn of each vessel A and B.

$\because \frac{1}{60}+\frac{1}{180}=\frac{4}{180}=\frac{1}{45}$, 45 turns of vessel A and 45 turns of vessel B will empty the tank completely. Hence, total number of turns = 45 + 45 = 90.

(Ans: 2)

Estimated Time to arrive at the answer = 60 seconds.

### Using Technique

Note that capacities of vessel A to that of B = 3 : 1. Hence in one turn of each 3x + 1x = 4x tank will be emptied (where ‘x’ the constant of proportionality). The tank in turn is $3x\times 60=180x$ large.
Hence, $\frac{180}{4}=45$ turns of each vessel will be needed. Hence total 90 turns are needed.