Daniel can plant an acre of corn in 6 hours. Working with Amanda, they can plant an acre of corn in 2 hours. How long would it take in hours for Amanda to plant an acre of corn by herself?
in six hours, they plant three acres (an acre each 2 hrs). But in those six hours, Dan planted one acre, so Amanda, the speedster, must have planted 5 acres.
Amanda rate 5 acres/6hrs or 5/6 acre/hr
so, her time for one acre is 6/5 hour.
Where did the 5 come from? Amanda planted 2 acres, while Dan planted 1.
1/2 = 1/A + 1/6
A = 3
You are right, I need to wear glasses at my computer.
In those six hours, Dan planted one acre, so Amanda planted two.
To solve this problem, we can use the concept of "work done per unit of time".
Let's assume that Amanda can plant an acre of corn in "x" hours by herself.
Now, let's calculate the work done by Daniel and Amanda working together in 1 hour. As per the given information, when they work together, they can plant an acre of corn in 2 hours. Therefore, in 1 hour, they complete 1/2 acre of corn.
Next, let's calculate the work done by Daniel alone in 1 hour. According to the information, Daniel can plant an acre of corn in 6 hours. Therefore, in 1 hour, Daniel completes 1/6 acre of corn.
Now, we need to find Amanda's work rate in 1 hour. Since the work done by Daniel and Amanda together in 1 hour is 1/2 acre and the work done by Daniel alone in 1 hour is 1/6 acre, we can subtract Daniel's work rate from the combined work rate to get Amanda's work rate.
Amanda's work rate = Combined work rate - Daniel's work rate
Amanda's work rate = 1/2 - 1/6
Amanda's work rate = 3/6 - 1/6
Amanda's work rate = 2/6
Amanda's work rate = 1/3 acre per hour
From the above calculation, we know that Amanda can plant 1/3 acre of corn in 1 hour.
Now, we can set up a proportion to find the time it would take for Amanda to plant an acre of corn by herself:
1 acre / (1/3 acre per hour) = x hours
To solve this proportion, we can multiply both sides by (1/3) to get:
x = 1 / (1/3)
x = 1 * (3/1)
x = 3
So, it would take Amanda 3 hours to plant an acre of corn by herself.