Mathematical Problem Solving

The first train travels for 1 hour before the second train leaves. In that time, it travels 60 miles. So, when the second train leaves, there are 240 miles left to travel. The two trains are traveling at a combined speed of 130 miles per hour. So, it will take them 2 hours to travel the remaining distance. Therefore, they will meet at 2:00 PM.

The farmer plants corn on 60% of the land, which is 0.6 * 100 = 60 acres. He plants soybeans on 20% of the land, which is 0.2 * 100 = 20 acres. Therefore, he plants wheat on 100 - 60 - 20 = 20 acres.

The area of a circle is given by the formula A = πr^2. Substituting r = 5 into the formula, we get A = π(5)^2 = 25π square inches.

We can use the Pythagorean theorem to find the length of the other leg. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs. In this case, the hypotenuse is 10 inches and one leg is 6 inches. So, the other leg is √(10^2 - 6^2) = √(100 - 36) = √64 = 8 inches.

60% of the employees are women, which is 0.6 * 100 = 60 employees. Therefore, the number of men is 100 - 60 = 40.

The discount is 20% of the original price, which is 0.2 * $20 = $4. Therefore, the sale price is $20 - $4 = $16.

The average speed is the total distance traveled divided by the total time taken. In this case, the total distance traveled is 240 miles and the total time taken is 4 hours. Therefore, the average speed is 240 miles / 4 hours = 60 mph.

The area of a rectangle is given by the formula A = lw. Substituting l = 12 feet and w = 8 feet into the formula, we get A = 12 feet * 8 feet = 96 square feet.

The first train travels for 1 hour before the second train leaves. In that time, it travels 70 miles. So, when the second train leaves, there are 20 miles left to travel. The two trains are traveling at a combined speed of 150 miles per hour. So, it will take them 20 miles / 150 miles per hour = 8/6 hours = 1 hour and 20 minutes to travel the remaining distance. Therefore, they will meet at 11:00 AM + 1 hour and 20 minutes = 12:20 PM.

40% of the employees are managers, which is 0.4 * 200 = 80 employees. 30% of the employees are engineers, which is 0.3 * 200 = 60 employees. Therefore, the number of technicians is 200 - 80 - 60 = 60.

The discount is 30% of the original price, which is 0.3 * $100 = $30. Therefore, the sale price is $100 - $30 = $70.

The average speed is the total distance traveled divided by the total time taken. In this case, the total distance traveled is 300 miles and the total time taken is 5 hours. Therefore, the average speed is 300 miles / 5 hours = 60 mph.

The area of a rectangle is given by the formula A = lw. Substituting l = 15 feet and w = 10 feet into the formula, we get A = 15 feet * 10 feet = 150 square feet.

The first train travels for 1 hour before the second train leaves. In that time, it travels 65 miles. So, when the second train leaves, there are 285 miles left to travel. The two trains are traveling at a combined speed of 140 miles per hour. So, it will take them 285 miles / 140 miles per hour = 2 hours and 5 minutes to travel the remaining distance. Therefore, they will meet at 10:00 AM + 2 hours and 5 minutes = 11:05 AM.

50% of the employees are women, which is 0.5 * 300 = 150 employees. Therefore, the number of men is 300 - 150 = 150.