Problem 1 - Fence Problem
A rancher owns land aside a river. He decides to enclose some of his land using fence. This enclosure must be rectangularly shaped with no fence along the river.
The maximum length of fence the rancher has available is 8,000 feet.
a) What should be the dimensions of the enclosure in order to maximize the area enclosed by the fence? Show graphical and mathematical solutions to this problem..
b) If any geometric shape (which can bound the river) is permitted, determine which shape would better maximize the area enclosed by the 8,000 feet of fence. Show you conclusions graphically and mathematically.
Problem Solving Steps
1. Study / Read Problem
2. Do Sketch
3. Define Variables
4. Write Equations / Inequalities
5. Solve Equations / Inequalities
6. Check Work
Problem 2 - Train Problem - Two trains depart Pueblo in opposite directions (north-south) with one train departing 45 minutes after the first train. The constant velocity of the train departing first was 62 mph. Calculate the required velocity of the other train if the distance between the 2 trains is 830 miles 7.5 hours after the first train departs.
Problem Solving Steps
1. Study / Read Problem
2. Do Sketch
3. Define Variables
4. Write Equations / Inequalities
5. Solve Equations / Inequalities
6. Check Work
Problem 3 - Radiator Problem - The T2000 Kenworth truck (shown to the right) has a radiator which will hold a maximum of 36 quarts of coolant. The manufacturer requires the coolant be a 50/50 mix of water and ethylene glycol (antifreeze). Presently, the radiator has 21 quarts of coolant with a mix of 41% of antifreeze and 59% of water.
You possess a container of a 55/45 mix of antifreeze/water. This container must be used to fill the radiator (completely) and bring it to a 50/50 mix.
1) How much of the 55/45 mix must be added to the radiator to obtain the required 50/50 mix in the radiator (and also a full radiator)?
2) Will any of the existing coolant have to be drained from the radiator before adding coolant from the 55/45 container?.
Problem Solving Steps
1. Study / Read Problem
2. Do Sketch
3. Define Variables
4. Write Equations / Inequalities
5. Solve Equations / Inequalities
6. Check Work
Problem 4 - Parking Lot Problem - Use the problem solving steps to solve the problem shown to the right. Show the steps and all work.
