Use the relationship distance＝speed×time in two equations.
Example ①
A journey from A to B covers 18 km and was made by bicycle and on foot. The bicycle speed was 12 km per hour, walking speed was 4 km per hour, and the total time was 2 hours. Find the distances traveled by bicycle and on foot.
Solution: Let the bicycle distance be x km and the walking distance be y km: { x+y=18、x/12+y/4=2. Equation 2 ×12: x+3y=24. ①−: 2y=6→y=3,x=15。15 km by bicycle and 3 km on foot
A journey from A to B covers 18 km and was made by bicycle and on foot. The bicycle speed was 12 km per hour, walking speed was 4 km per hour, and the total time was 2 hours. Find the distances traveled by bicycle and on foot.
Solution: Let the bicycle distance be x km and the walking distance be y km: { x+y=18、x/12+y/4=2. Equation 2 ×12: x+3y=24. ①−: 2y=6→y=3,x=15。15 km by bicycle and 3 km on foot
Example ②（Meeting and Chasing）
Two people leave points A and B (60 km apart) at the same time. The person traveling from A to B travels at 40 km per hour, and the person traveling from B to A travels at 20 km per hour. After how many hours will they meet?
Solution: If they meet after t hours, 40t+20t=60→60t=60→t=1。After 1 hour
Two people leave points A and B (60 km apart) at the same time. The person traveling from A to B travels at 40 km per hour, and the person traveling from B to A travels at 20 km per hour. After how many hours will they meet?
Solution: If they meet after t hours, 40t+20t=60→60t=60→t=1。After 1 hour
Key Points
- Arrange distance＝speed×time and set up two equations
- Use consistent units (km/h, m/min)
- If fractions appear, multiply by the LCM to convert them into integers
Practice Problem
- A 10 km journey was made on foot at 5 km per hour going there and by bicycle at 10 km per hour returning. The total time was 3 hours. Find the times for going and returning.
Answer and Explanation
- Answer:2 hours going and 1 hour returning. { x+y=3、5x+10y=10（The total distance is not always 10km×2; the outward and return trips use separate equations.）。Correctly, for the distances: 5x=10,10y=10… This is the same 10 km route in each direction. x=2,y=1。