Problem Solving: Time/Rate Flashcards

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?

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.

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?

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.

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?

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.

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?

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.

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?

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.

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?

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.