Fly #5

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1)A homeowner estimates that it will take 9 days to roof his house. A professional roofer estimates that he could roof the house in 5 days. How long will it take if the homeowner helps the roofer?

2)A plane can fly 300 miles in the same time as it takes a car to go 120 miles. If the car travels 90 mph slower than the plane, find the speed of the plane?

3)A plane can fly 235 miles downwind in the same amount of time as it can travel 165 miles upwind. Find the velocity of the wind if the plane can fly 200 mph in still air?

4)Two bond funds pay interest at rates that differ by 2%. Money invested for one year in the first fund earns $540 interest. The same amount invested in the other fund earns $660. Find the lower rate of interest.

(1)
A homeowner can complete 1/9 of a roof in one day. A roofer can do 1/5 in one day. Working together, they can do (1/9 + 1/5) roofs per day, or:

5/45 + 9/45 = 14/45 roofs per day. This means it will take them 45/14 days to do the job, or just over 3 days.

(2)
The plane can go 300 miles at x miles per hour in the same amount of time that the car can go 120 miles at x-90 miles per hour.

300 / x = 120 / (x - 90)
120x = 300x - 27000
-180x = -27000
180x = 27000
x = 150

The plane is going 150 miles an hour. The car is going 60 miles an hour.

(3)
Set up just like (2), with (distance) / (speed)

235 / (200 + x) = 165 / (200 - x)
33000 + 165x = 47000 - 235x
400x = 14000
x = 35

The wind speed is 35 mph. (This is much more obvious in the question but I figured I would do it out to reinforce these ratio problems).

(4)
Set up just like (2), with (interest earned) / (rate)

540 / x = 660 / x + 2
660x = 540x + 1080
120x = 1080
x = 9

The lower rate is 9%, the higher rate is 11%.

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