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It’s the first day of summer, and the Johnson family wants to fill their new backyard pool. They start with the pool already 1/8 full from recent rain. After running their garden hose for several hours, they manage to fill the pool to 3/4 full.
a) What fraction of the pool was filled by the water from the garden hose? Hint: Use equivalent fractions.
b) If the water added from the hose amounts to 3300 liters, how many liters of water were already in the pool from the rain?
c) Based on your findings in parts (a) and (b), what is the total capacity of the Johnson family’s pool in liters?
d) If their garden hose can deliver 15 liters per minute, how long did it take to fill the pool to 3/4 full? Give your answer in hours and minutes, rounded to the nearest minute.
a) To find the fraction filled by the hose:
– Initial pool level: 1/8 = 2/16
– Final pool level: 3/4 = 12/16
– Fraction filled by hose: 12/16 – 2/16 = 10/16 = 5/8
b) To find the amount of water from rain:
– Hose added 5/8 of the pool, which is 3300 liters
– So 1/8 of the pool is 3300 ÷ 5 = 660 liters
– The rain filled 1/8 of the pool, so there were 660 liters from rain
c) To calculate the total capacity of the pool:
– 1/8 of the pool is 660 liters
– So the full pool (8/8) is 660 × 8 = 5280 liters
d) To calculate the time taken to fill the pool:
– Water added by hose: 3300 liters
– Hose flow rate: 15 liters per minute
– Time taken: 3300 ÷ 15 = 220 minutes
– In hours and minutes: 3 hours and 40 minutes
Therefore, it took 3 hours and 40 minutes to fill the pool to 3/4 full.
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