Sarah picks a bushel of apples in 45 min. Andy picks a bushel of apples in 75 min. How long will it take them to pick a bushel together?
Let x be the time it takes for Sarah and Andy to pick a bushel together.
Sarah's picking rate is 1 bushel/45 min = 1/45 bushel/min.
Andy's picking rate is 1 bushel/75 min = 1/75 bushel/min.
Together, their picking rate is the sum of their individual rates:
1/45 + 1/75 = 5/225 + 3/225 = 8/225 bushel/min.
Using the formula: rate × time = work, we have:
(8/225) × x = 1
Solving for x, we get:
x = 225/8 min ≈ 28.125 min.
Therefore, it will take Sarah and Andy about 28.125 min (or 28 min and 8.5 sec) to pick a bushel of apples together.
To find out how long it will take Sarah and Andy to pick a bushel of apples together, we can use the concept of rates.
Let's start by finding their individual rates of picking apples:
Sarah's rate = 1 bushel / 45 min
Andy's rate = 1 bushel / 75 min
To determine their combined rate, we can add up their individual rates:
Combined rate = Sarah's rate + Andy's rate
Combined rate = 1 bushel / 45 min + 1 bushel / 75 min
Now, let's find a common denominator to add the rates together. The least common multiple of 45 and 75 is 225, so we can multiply each rate by the appropriate factor to get the common denominator of 225.
Combined rate = (1 bushel / 45 min) * (5 / 5) + (1 bushel / 75 min) * (3 / 3)
= 5 bushels / 225 min + 3 bushels / 225 min
= 8 bushels / 225 min
Finally, we can find the time it will take for them to pick a bushel together by taking the reciprocal of the combined rate:
Time = 1 / Combined rate
= 225 min / 8 bushels
Therefore, it will take Sarah and Andy approximately 28.125 min (or rounded to the nearest whole minute - 28 min) to pick a bushel of apples together.