SOLUTION: My brain is fried studying for finals and I'm stumped on 2 word problems that are seemingly simple. 1. A small plane went 240 miles in 3 hours flying against the wind and the s

Question 321880: My brain is fried studying for finals and I'm stumped on 2 word problems that are seemingly simple.
1. A small plane went 240 miles in 3 hours flying against the wind and the same amount of time to go 300 miles with the wind. What was the speed of the plane without the wind?
2. It takes Danny 3 times as long to mow a field as it takes his father. Together they can mow the same field in 4 hours. How long does it take Danny working alone?
Please and thank you,
"An A math student who just can't think anymore"
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
1. A small plane went 240 miles in 3 hours flying against the wind and the same amount of time to go 300 miles with the wind. What was the speed of the plane without the wind?
240/3 = 80 mph
300/3 = 100 mph
The airspeed of the plane is the average, 90 mph.
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2. It takes Danny 3 times as long to mow a field as it takes his father. Together they can mow the same field in 4 hours. How long does it take Danny working alone?
Danny takes 3x hours
Father takes x hours
--------------------
Danny does 1/3x of the field per hour.
His father does 1/x per hour.
Together, they do 1/(3x) + 1/x per hour, = 4/(3x) fields per hour.
4/(3x) fields per hour --> 3x/4 hours per field
3x/4 = 4
3x = 16
x = 16/3
Danny takes 3x, = 16 hours.

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