Frank and Hank are farmers. Frank can plant a field in 3 hours, but when he works with Hank, they
can plant a field in 1 hour. How long, in minutes, would it take Hank to plant a field by himself?
franks rate = 1/3
Hanks rate = 1/x
combined rate = 1/3 + 1/x
= (x+3)/(3x)
1/( (x+3)/(3x) ) = 1
3x/(x+3) = 1
3x = x + 3
2x = 3
x = 1.5
It would take him 1.5 hours
1st grade or waht
To find out how long it would take Hank to plant a field by himself, we need to determine his individual working rate. We know that when working together, Frank and Hank can plant a field in 1 hour.
Let's assume that Hank's individual working rate is represented by x. Therefore, Frank's individual working rate is 1/3 fields per hour, and their combined working rate is 1 field per hour.
To express this mathematically, we can create the following equation:
1/3 + x = 1
Now, we can solve for x to find Hank's individual working rate:
x = 1 - 1/3
x = 2/3
Hank's individual working rate is 2/3 fields per hour.
To find the time it would take Hank to plant a field by himself, we can use the formula:
Time = 1 / Rate
Time = 1 / (2/3)
To divide by a fraction, we can multiply by its reciprocal:
Time = 1 * (3/2)
Time = 3/2
So, it would take Hank 3/2 of an hour to plant a field by himself.
Finally, to convert this into minutes, we multiply by 60 since there are 60 minutes in an hour:
Time = (3/2) * 60
Time = 90 minutes
Therefore, it would take Hank 90 minutes to plant a field by himself.