CFAT - Canadian Forces Aptitude Problem Solving: Word Problems Questions and Answers 1 — Questions and Answers
Question 1: A military convoy travels from Base A to Base B. The first 180 km of the trip is on a paved highway at an average speed of 90 km/h. The remaining 70 km is on a dirt road at an average speed of 40 km/h. What is the total travel time for the entire journey?
- 3 hours, 15 minutes
- 3 hours, 45 minutes (Correct answer)
- 4 hours
- 2 hours, 50 minutes
Correct answer: 3 hours, 45 minutes
The problem must be solved in two parts. First, calculate the time for the highway portion: Time = Distance / Speed = 180 km / 90 km/h = 2 hours. Second, calculate the time for the dirt road portion: Time = 70 km / 40 km/h = 1.75 hours. The total travel time is the sum of the two parts: 2 hours + 1.75 hours = 3.75 hours. To convert 0.75 hours to minutes, multiply by 60 (0.75 * 60 = 45 minutes). The total time is 3 hours and 45 minutes.
Question 2: A supply depot has a total of 54 containers of water and ration packs. The number of water containers is 6 less than three times the number of ration pack containers. How many water containers are at the depot?
- 15
- 18
- 39 (Correct answer)
- 42
Correct answer: 39
Let W be the number of water containers and R be the number of ration pack containers. We can set up two equations: (1) W + R = 54 and (2) W = 3R - 6. Substitute the second equation into the first: (3R - 6) + R = 54. This simplifies to 4R - 6 = 54. Add 6 to both sides to get 4R = 60. Divide by 4 to find R = 15. The question asks for the number of water containers (W), so substitute R back into the first equation: W + 15 = 54, which gives W = 39.
Question 3: A recruit's average score on the first three marksmanship tests was 84. To raise their overall average to exactly 87 after the fourth test, what score must they achieve on that fourth test?
- 96 (Correct answer)
- 87
- 90
- 93
Correct answer: 96
First, calculate the total score from the first three tests: 3 tests * 84 average = 252 total points. Next, calculate the desired total score for all four tests: 4 tests * 87 desired average = 348 total points. The score needed on the fourth test is the difference between the desired total and the current total: 348 - 252 = 96.
Question 4: A company of 150 soldiers is preparing for a mission. 10% of the soldiers are assigned to vehicle maintenance. Of the remaining soldiers, one-third are assigned to guard duty. How many soldiers are left for the main mission force?
- 135
- 100
- 45
- 90 (Correct answer)
Correct answer: 90
First, calculate the number of soldiers on vehicle maintenance: 10% of 150 is 15. Subtract this from the total to find the remaining soldiers: 150 - 15 = 135. Next, calculate the number on guard duty from the remainder: one-third of 135 is 45. Finally, subtract the guard duty soldiers from the remaining number to find the final count for the main mission: 135 - 45 = 90.
Question 5: Corporal Smith can assemble a standard field tent in 3 hours. Private Jones can assemble the same tent in 5 hours. If they work together, how long will it take them to assemble one tent?
- 2 hours
- 4 hours
- 1 hour, 52.5 minutes (Correct answer)
- 8 hours
Correct answer: 1 hour, 52.5 minutes
Calculate the individual work rates per hour. Corporal Smith's rate is 1/3 of a tent per hour, and Private Jones's rate is 1/5 of a tent per hour. Their combined rate is (1/3) + (1/5) = 8/15 of a tent per hour. To find the total time, take the reciprocal of the combined rate: Time = 1 / (8/15) = 15/8 hours, which is 1.875 hours. Converting the decimal to minutes: 0.875 * 60 = 52.5 minutes. Therefore, the total time is 1 hour and 52.5 minutes.
Question 6: A small engine requires a fuel-to-oil mixture in a 50:1 ratio. To prepare 10.2 litres of this mixture, how many millilitres of oil are needed? (Note: 1 litre = 1000 millilitres)
- 200 ml (Correct answer)
- 204 ml
- 250 ml
- 510 ml
Correct answer: 200 ml
The ratio 50:1 means there are 50 parts of fuel for every 1 part of oil, making a total of 51 parts in the mixture. First, convert the total volume to millilitres: 10.2 litres * 1000 ml/litre = 10200 ml. To find the volume of one 'part', divide the total volume by the total number of parts: 10200 ml / 51 parts = 200 ml per part. Since the oil represents 1 part of the mixture, 200 ml of oil is needed.
CFAT - Canadian Forces Aptitude Problem Solving: Word Problems Questions and Answers 1
A military convoy travels from Base A to Base B.
The first 180 km of the trip is on a paved highway at an average speed of 90 km/h.
The remaining 70 km is on a dirt road at an average speed of 40 km/h.
What is the total travel time for the entire journey?