Worded Problems / Plane and Solid Geometry: Solve the following problems and show your solution.

1. At what time after 5 o'clock in the morning will the hands of the clock be a) perpendicular for the first time? b) opposite for the first time?

2. What time between 2 and 3 o'clock will the angle between the hands of the clock be bisected by the line connecting the center of the clock and the 3 o'clock mark?

3. An airplane went 360 mile in 2 hours with the wind and flying back the same route, it took 3 and 3/5 hours against the wind. Determine the velocity of the wind.

4. In a box, there are 25 coins consisting of quarters, nickels and dimes with a total amount of 2.75 dollars. If nickels were dimes, the dimes were quarters and the quarters were nickels, the total amount would be 3.75 dollars. How many quarters are there?

5. A two digit number is equal to 8 times the sum of its digits. If 45 is subtracted from the number, its digits are reversed. What is the number?

6. The denominator of a certain fraction is three more than twice the number. If 7 is added to both terms of the fraction, the resulting fraction is 3/5. Find the original number.

7. A man is 41 years old and his son is 9. In how many years will the father be three times as old as his son?

8. Farmer A can plow the field in 4 days by using a tractor. Farmer B can plow the same field in 6 days using a carabao. How long will it take to plow a field if they work together?

9. For a particular experiment you need 5liters of a 10% solution. You find 7% and 12% solution on the shelves. How much of the 7% solution should you mix with the appropriate mount of the 12% solution to get 5 liters of a 10% solution?

10. The fertilizer used for crops contains two important components namely, nitrogen and phosphate. Fertilizer A is 20% nitrogen and 2% phosphate. Fertilizer B is 15% nitrogen and 6% phosphate. Fertilizer C is 30% nitrogen and zero phosphate. How many kilograms of each should be mixed to make 20 kg of fertilizer that is 19% nitrogen and 4% phosphate?