Problem 1:

Ella and Tom start from the same point and walk in opposite directions. Ella walks west at a speed of 4 km/h, and Tom walks east at a speed of 6 km/h. How far apart will they be after 3 hours?

Solution: To solve this problem, you need to calculate the distance each person travels and then add these distances together since they are moving in opposite directions.

1. Ella’s Speed: 4 km/h
2. Tom’s Speed: 6 km/h
3. Time: 3 hours

Calculating Distance:

• Distance Traveled by Ella: Ella’s speed multiplied by the time traveled.

  Distance by Ella = 4 km/h × 3h = 12 km 

• Distance Traveled by Tom: Tom’s speed multiplied by the time traveled.

  Distance by Tom = 6 km/h × 3h = 18 km 

Total Distance Apart: Add the distances traveled by Ella and Tom to find the total distance they are apart after 3 hours.

Problem 3:

A car travels from City A to City B, a distance of 180 kilometers. The car travels the first half of the journey at an average speed of 60 km/h and the second half at an average speed of 90 km/h. What is the average speed of the car for the entire journey?

Solution: To calculate the average speed for the entire journey, find the total time taken for each half of the journey and then use the total time and total distance to find the average speed.

Problem 4

Problem: Jill and Sam start running on a 400-meter circular track from the same point but in opposite directions. Jill runs at a speed of 8 meters per second, while Sam runs at a speed of 5 meters per second. How long will it take before they meet again at the starting point?

Solution: To solve this problem, determine how fast Jill and Sam are separating from each other and calculate how quickly they complete a circuit to meet back at the start.

Combined Speed: Since they are running in opposite directions, their speeds add up.

Time to Meet: The time it takes for them to meet can be calculated by dividing the track’s total distance by their combined speed.

Conclusion: Jill and Sam will meet again at the starting point approximately 30.77 seconds after they start running.

Problem 5

Problem: Two cars are traveling towards each other from two cities that are 300 kilometers apart. The first car travels at 70 km/h and the second car at 80 km/h. How long will it take for the two cars to meet?

Solution: To determine when the cars will meet, calculate their combined approach speed and use this to find the time needed for them to cover the 300 kilometers separating them.

Combined Approach Speed: The speeds of the two cars add together because they are moving towards each other.

Time to Meet: The time to meet is calculated by dividing the total distance by the combined approach speed.