Question13.
Hector used a tool called an auger to remove corn from a storage bin at a constant rate. The bin contained 24,000 bushels of corn when Hector began to use the auger. After 5 hours of using the auger, 19,350 bushels of corn remained in the bin. If the auger continues to remove corn at this rate, what is the total number of hours Hector will have been using the auger when 12,840 bushels of corn remain in the bin?
Studdy Solution
STEP 1
What is this asking? How long will it take for an auger removing corn at a constant rate to leave 12,840 bushels, if it started with 24,000 bushels and had 19,350 bushels left after 5 hours? Watch out! Don't mix up the bushels removed with the bushels remaining!
STEP 2
1. Calculate the rate of corn removal.
2. Calculate the time to reach the desired amount.
STEP 3
Alright, so Hector's got this awesome auger, and it's munching away at the corn!
We know the **initial amount** was bushels, and after hours, there were bushels left.
Let's find out how much corn the auger ate in those hours!
STEP 4
The amount removed is the **initial amount** minus the **remaining amount**: bushels.
So, the auger gobbled up bushels in hours.
STEP 5
Now, to find the *rate* at which the auger removes corn, we divide the **total bushels removed** by the **time it took**: bushels/hour.
That's one hungry auger!
STEP 6
We want to know how long it takes to have bushels left.
First, let's figure out how much corn needs to be removed to get to that amount.
We start with bushels and want to end up with , so we subtract the **desired amount** from the **initial amount**: bushels.
STEP 7
We know the rate is bushels/hour, and we need to remove bushels.
To find the time, we divide the **total bushels to be removed** by the **rate of removal**: .
STEP 8
It will take Hector **12 hours** to have 12,840 bushels of corn remaining in the bin.
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