CALLING ALL JESUS HELPERS Bonus Problem 2. A pump fills an empty pool at a rate of 500 cubic meters per hour. If one liter is equivalent to one cubic decimeter and 1 meter is equal to 10 decimeters, how many liters of water are in the pool half an hour after the pump starts?

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250,000 L

Step-by-step explanation:

we are given the fill rate of 500 m³ per hour , i.e.

in 1 hour > 500 m³ would have been added

if the fill rate is constant, then it reasons that in 1/2 hour, we would expect to see only 1/2 volume of water compared to a full hour , hence:

in 1/2 hour > 1/2  x 500 m³ = 250m³ would have been added

The question wants the answer in liters, however we have just calculated the volume in m³ above. Hence we need to convert 250m³ into liters

We note that 1 m³

= 1 m x 1 m x 1 m ( we are given that 1 meter is equal to 10 decimeters. substitute this into the equation,)

= 10 dm x 10 dm x 10 dm

= 1000 dm³

therefore 250m³ = 250 m³ x 1000 dm³ per m³= 250,000 dm³

we are further given that:

1 dm³ = 1 L, hence

250,000 dm³ = 250,000L

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step-by-step explanation:

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)