CFAT - Canadian Forces Aptitude Problem Solving: Time/Rate Questions and Answers 1 — Questions and Answers
Question 1: A military supply truck travels from Base A to Base B, a distance of 120 km, at a speed of 60 km/h. It returns from Base B to Base A along the same route at a speed of 40 km/h. What is the average speed for the entire round trip?
- 48 km/h (Correct answer)
- 50 km/h
- 52 km/h
- 100 km/h
Correct answer: 48 km/h
Average speed is calculated by dividing the total distance by the total time. The trip to Base B takes 120 km / 60 km/h = 2 hours. The return trip takes 120 km / 40 km/h = 3 hours. The total distance is 120 km + 120 km = 240 km. The total time is 2 hours + 3 hours = 5 hours. Therefore, the average speed is 240 km / 5 hours = 48 km/h.
Question 2: A machine at a factory produces 150 bolts in 3 minutes. At this constant rate, how many bolts can the machine produce in 2 hours?
- 3,000
- 6,000 (Correct answer)
- 4,500
- 9,000
Correct answer: 6,000
First, calculate the machine's production rate per minute: 150 bolts / 3 minutes = 50 bolts per minute. Next, convert the total time to minutes: 2 hours * 60 minutes/hour = 120 minutes. Finally, multiply the rate by the total time to find the total output: 50 bolts/minute * 120 minutes = 6,000 bolts.
Question 3: A team of two, Alex and Ben, can complete a project in 10 days. Alex, working alone, can complete it in 15 days. They work together for 6 days, after which Alex leaves. How many days will it take Ben to finish the remaining work?
- 9 days
- 15 days
- 12 days (Correct answer)
- 6 days
Correct answer: 12 days
First, find Ben's individual rate. The combined rate is 1/10 project/day, and Alex's rate is 1/15 project/day. Ben's rate is (1/10) - (1/15) = 1/30 project/day. In 6 days together, they complete 6 * (1/10) = 6/10 or 3/5 of the project. The remaining work is 1 - 3/5 = 2/5 of the project. The time for Ben to finish is Work / Rate = (2/5) / (1/30) = (2/5) * 30 = 12 days.
Question 4: A water tank can be filled by an inlet pipe in 5 hours. It can be emptied by an outlet pipe in 8 hours. If the tank is empty and both pipes are opened simultaneously, how long will it take to fill the tank?
- 3 hours
- 6.5 hours
- 24 hours
- 13 hours and 20 minutes (Correct answer)
Correct answer: 13 hours and 20 minutes
The inlet pipe fills at a rate of 1/5 of the tank per hour. The outlet pipe drains at a rate of 1/8 of the tank per hour. The net filling rate is the difference: 1/5 - 1/8 = 8/40 - 5/40 = 3/40 of the tank per hour. The time to fill the entire tank is the reciprocal of this rate: Time = 1 / (3/40) = 40/3 hours, which is 13 and 1/3 hours, or 13 hours and 20 minutes.
Question 5: Two soldiers start at opposite ends of a 30 km road. Soldier A walks at a speed of 4 km/h, and Soldier B walks at a speed of 6 km/h. If they both start at the same time and walk towards each other, how long will it take for them to meet?
- 3 hours (Correct answer)
- 5 hours
- 2.5 hours
- 7.5 hours
Correct answer: 3 hours
Since the soldiers are walking towards each other, their relative speed is the sum of their individual speeds: 4 km/h + 6 km/h = 10 km/h. To find the time it takes for them to meet, divide the initial distance by their combined speed: Time = 30 km / 10 km/h = 3 hours.
Question 6: One soldier can dig a standard trench in 4 hours. A second soldier can dig the same type of trench in 6 hours. If they work together, how long will it take them to dig one trench?
- 5 hours
- 10 hours
- 2 hours and 24 minutes (Correct answer)
- 2 hours and 30 minutes
Correct answer: 2 hours and 24 minutes
The first soldier's rate is 1/4 of the trench per hour. The second soldier's rate is 1/6 of the trench per hour. Their combined rate is 1/4 + 1/6 = 3/12 + 2/12 = 5/12 of the trench per hour. To find the time to complete one trench, take the reciprocal of the combined rate: Time = 1 / (5/12) = 12/5 hours, which is 2.4 hours. Converting 0.4 hours to minutes (0.4 * 60) gives 24 minutes.
CFAT - Canadian Forces Aptitude Problem Solving: Time/Rate Questions and Answers 1
A military supply truck travels from Base A to Base B, a distance of 120 km, at a speed of 60 km/h.
It returns from Base B to Base A along the same route at a speed of 40 km/h.
What is the average speed for the entire round trip?