It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impatient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes 5 minutes to fill the pool. Which equation can be used to determine r , the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?
Answer
A
5 eighths plus 5 r is equal to 1
B
5 eighths is equal to 5 r
C
5 times 5 eighths is equal to r
D
5 eighths plus 5 r is equal to 8
Explanation
The hose fills 1/8 of the pool per minute because it takes 8 minutes to fill the whole pool. When the hose and sprinkler work together, they fill 1/5 of the pool per minute. So their combined rate is 1/8 + r = 1/5; multiplying both sides by 5 gives 5/8 + 5r = 1. This is choice A, “5 eighths plus 5r is equal to 1.”
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