AnswersTransition Mathematics for SeniorsSolving Rate Problems — QuizQuestion 10
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Solving Rate Problems — Quiz

Question 10 • Transition Mathematics for Seniors

It takes 5 minutes to fill the sink using only the cold water. If both the hot water and the cold water are turned on, it takes 2 minutes to fill the sink. Which is the correct table that can be used to determine x , the time in minutes it takes to fill the sink using only the hot water?

Answer
A
Table with 4 columns and 3 rows.Row 1: Column 1, empty; Column 2, 'Rate (part/min)'; Column 3, 'Time (min)'; Column 4, 'Part of Sink Filled' Row 2: Column 1, 'Cold'; Column 2, '2'; Column 3, '5'; Column 4, '10' Row 3: Column 1, 'Hot'; Column 2, 'x'; Column 3, '5'; Column 4, '5 x'
B
Table with 4 columns and 3 rows.Row 1: Column 1, empty; Column 2, 'Rate (part/min)'; Column 3, 'Time (min)'; Column 4, 'Part of Sink Filled' Row 2: Column 1, 'Cold'; Column 2, '1 half'; Column 3, '5'; Column 4, '5 halves' Row 3: Column 1, 'Hot'; Column 2, '1 over x'; Column 3, '5'; Column 4, '5 over x'
C
Table with 4 columns and 3 rows.Row 1: Column 1, empty; Column 2, 'Rate (part/min)'; Column 3, 'Time (min)'; Column 4, 'Part of Sink Filled' Row 2: Column 1, 'Cold'; Column 2, '5'; Column 3, '2'; Column 4, '10' Row 3: Column 1, 'Hot'; Column 2, 'x'; Column 3, '2'; Column 4, '2 x'
D
Table with 4 columns and 3 rows.Row 1: Column 1, empty; Column 2, 'Rate (part/min)'; Column 3, 'Time (min)'; Column 4, 'Part of Sink Filled' Row 2: Column 1, 'Cold'; Column 2, '1 fifth'; Column 3, '2'; Column 4, '2 fifths' Row 3: Column 1, 'Hot'; Column 2, '1 over x'; Column 3, '2'; Column 4, '2 over x'

Explanation

A rate is the fraction of the sink filled per minute. The cold tap fills 1 sink in 5 minutes, so its rate is 1/5 sink per minute; the hot tap’s rate is 1/x. Since both taps run for 2 minutes, the table should show 2/5 and 2/x of the sink filled, as in choice D.

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