Working together, Sarah and Jeff can do a task in 6 hours. Jeff uses a motorized cart to do the task, whereas Sarah uses a pushcart. If each person does the task without the help of the other, it takes Sarah twice as long as it takes Jeff. How long does it take Sarah to complete the task?
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this is very similar, except you would have
1/x and 1/2x as the combined rate, and you know that result.
To solve this problem, we can assign variables to the unknown quantities and set up equations based on the given information.
Let's say Jeff takes 'x' hours to complete the task alone. According to the problem, it takes Sarah twice as long as Jeff, so it takes Sarah '2x' hours to complete the task alone.
When they work together, they can complete the task in 6 hours, so the combined work rate is 1/6 of the task per hour. We can set up the following equation based on their individual work rates:
1/x + 1/(2x) = 1/6
To simplify this equation, we can find the common denominator, which is 6x:
(6 + 3) / (6x) = 1/6
9 / (6x) = 1/6
Cross-multiplying, we get:
9 = 6x
Now, dividing both sides by 6, we find:
x = 9/6 = 3/2
So, Jeff takes 3/2 hours (or 1.5 hours) to complete the task alone.
To find Sarah's time, we can substitute this into the equation we set up earlier:
2x = 2 * (3/2) = 3
Therefore, it takes Sarah 3 hours to complete the task alone.