CFAT - Canadian Forces Aptitude Problem Solving: Time/Rate 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?

Accepted Answer

48 km/h

Answer

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?

Accepted Answer

6,000

Answer

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?

Accepted Answer

12 days

Answer

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?

Accepted Answer

13 hours and 20 minutes

Answer

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?

Accepted Answer

3 hours

Answer

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.

(CFAT) Canadian Forces Aptitude Test Practice Test

(CFAT) Canadian Forces Aptitude Test Practice Test

CFAT - Canadian Forces Aptitude Problem Solving: Time/Rate Questions and Answers