rate

[ROHIT11111]

7. A rectangular swimming pool is 30 metres long and 10 metres wide. The pool is empty and is being filled at a rate of 16,000 litres per hour. After 15 hours, how deep is the water in the pool in metres? (1000 litres = 1 cubic metre). 

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Hi ROHIT11111,

Have you transcribed this question correctly? I ask because the correct answer is a bit 'weird' relative to the rest of the information in the prompt. Also, when posting GMAT questions, you should post the 5 answer choices with the question. Sometimes the 'design' of the answer choices can help you to avoid a long-winded 'math approach.' With just the prompt, we have no choice but to do that math. This is essentially a 'rate' question with a little bit of geometry thrown in.

We know the length and width of the pool, so we know that it's surface area is (30)(10) = 300 square meters.

IF... the pool was 1 meter deep, then that pool would hold (30)(10)(1) = 300 cubic meters of water. By changing the depth, we change the volume of water that the pool can hold.

We're told that the pool starts off empty, then is filled at a rate of 16,000 liters per hour for 15 hours. That is a total of...

(16,000)(15) = 240,000 liters of water.

Since 1000 liters = 1 cubic meter of water....

240,000 liters = 240 cubic meters of water

We can now solve for the depth of the pool...

(30)(10)(Depth) = 240 cubic meters
300(Depth) = 240
Depth = 240/300 = 4/5 of a meter

GMAT assassins aren't born, they're made,
Rich

[OptimusPrep]

7. A rectangular swimming pool is 30 metres long and 10 metres wide. The pool is empty and is being filled at a rate of 16,000 litres per hour. After 15 hours, how deep is the water in the pool in metres? (1000 litres = 1 cubic metre). 

Amount of water filled in 15 hours = 16000*15 = 240,000 lts.
This tells us the volume of the pool filled.

We have the length and breadth and simply need to find out the height.
We know that volume = l*b*h

Therefore height = 240,000 lts. /30m*10m
Converting everything in the same units,

Remember
1lt = 1000cc


Height = 240,000*1000 / 300*100*100 cm
Height = 800 centimetres
Or Height = 0.8 meters.