4. A small airplane flies at speed r if there is no wind. (All speeds in miles per hour.) But there is a 20MPH wind.
(i) What is the airplane’s speed with the wind, and what is its speed against the wind. Answer in a complete English sentence that includes the UNITS.
(ii) Two cities are 600 miles apart, and the airplane makes a round trip, all the while the 20MPH wind blows. Find the time of each leg of the trip. Answer this too in a complete English sentence that includes the UNITS.
(iii) Suppose now you know that the trip against the wind requires exactly 1 hour more than the trip with the wind. Use (ii) to find r.
(iv) Now solve for r. Find it both in simplest radical form, and as a decimal estimate.
(v) If flight safety rules require a two hour break between legs of the round trip, find the total time of the trip. And when you are done, write the answer in a complete English sentence.
5. Suppose for the trip against the wind in 4., you must make the trip in between 125 and 150 minutes, and the airplane’s normal speed is v. Wind is as always 20 MPH.
(i) Convert these times to fractions of an hour.
(ii) Now set up a compound inequality that involves v.
(iii) Solve your inequality for the fastest and slowest permissible speeds.
(iv) Again, write your answer in a complete English sentence that includes units.
2. Suppose we have concentric circles, the inner of radius r, and the outer circle having radius five units greater than the inner.
(i) Draw and label a sketch of the figure described above.
(ii) Now suppose you know that the area of the doughnut region is exactly 100?. Write an equation that you can solve for r.
(iii) Now solve it for r.
(iv) Next, find the exact area of the big circle.
(i) What is the airplane’s speed with the wind, and what is its speed against the wind. Answer in a complete English sentence that includes the UNITS.
(ii) Two cities are 600 miles apart, and the airplane makes a round trip, all the while the 20MPH wind blows. Find the time of each leg of the trip. Answer this too in a complete English sentence that includes the UNITS.
(iii) Suppose now you know that the trip against the wind requires exactly 1 hour more than the trip with the wind. Use (ii) to find r.
(iv) Now solve for r. Find it both in simplest radical form, and as a decimal estimate.
(v) If flight safety rules require a two hour break between legs of the round trip, find the total time of the trip. And when you are done, write the answer in a complete English sentence.
5. Suppose for the trip against the wind in 4., you must make the trip in between 125 and 150 minutes, and the airplane’s normal speed is v. Wind is as always 20 MPH.
(i) Convert these times to fractions of an hour.
(ii) Now set up a compound inequality that involves v.
(iii) Solve your inequality for the fastest and slowest permissible speeds.
(iv) Again, write your answer in a complete English sentence that includes units.
2. Suppose we have concentric circles, the inner of radius r, and the outer circle having radius five units greater than the inner.
(i) Draw and label a sketch of the figure described above.
(ii) Now suppose you know that the area of the doughnut region is exactly 100?. Write an equation that you can solve for r.
(iii) Now solve it for r.
(iv) Next, find the exact area of the big circle.
