Lesson 14: Distance and Time Calculations

§Text Passage

1Summary 重點摘要

Learn to use speed formula to calculate distance and time, plus timetable problems: what time does the bus arrive, how long has it travelled.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Block 1: Calculate DistanceTo find distance use d = v × t. Example: at 50 km/h for 3 hours, distance = 50 × 3 = 150 km. If the time is three and a half hours, first write it as 3.5 hours and work out 50 × 3.5 = 175 km. With half hours in the question, convert before multiplying to avoid slips. If the speed is 80 m/s for 12 seconds, distance = 80 × 12 = 960 m; the formula is unchanged, only the units become metres and seconds, so read the units the question uses first.
2. Block 2: Calculate TimeTo find time use t = d ÷ v. Example: for 120 km at 60 km/h, time = 120 ÷ 60 = 2 hours. If the division gives a decimal such as 2.25 hours, change it into '2 hours 15 minutes' so the answer is clear. Another example: for 45 km at a walking pace of 9 km/h, time = 45 ÷ 9 = 5 hours; the smaller the speed, the longer the journey takes — a quick way to judge whether an answer is reasonable.
3. Block 3: Decimal Hours to Hours and MinutesTo change a decimal number of hours into hours and minutes, multiply the decimal part by 60. Example: 0.5 hour = 0.5 × 60 = 30 minutes; 0.25 hour = 15 minutes; 0.75 hour = 45 minutes. So 2.25 hours = 2 hours 15 minutes, and 3.5 hours = 3 hours 30 minutes. Another example: 1.2 hours = 0.2 × 60 = 12 minutes, that is 1 hour 12 minutes; since 0.1 hour = 6 minutes, every extra 0.1 in the decimal part adds 6 minutes.
4. Block 4: Timetable (Arrival Time)To find an arrival time, add: departure time + travel time = arrival time. Example: leaving at 9:15 and travelling 45 minutes brings the clock to 10:00, so the arrival time is 10:00. Be careful when the journey crosses noon or midnight; add in stages if needed. Another example: leaving at 22:50 and travelling 40 minutes — add 10 minutes to reach 23:00, then 30 more to reach 23:30, so the arrival time is 23:30; near midnight, adding in stages is safest.
5. Block 5: Timetable (Travel Time)To find the travel time, subtract: arrival time - departure time = travel time. Example: departing at 8:00 and arriving at 9:20 gives 1 hour 20 minutes. If the two times fall on different days, for example 23:30 to 0:30, add 24 hours first before subtracting. Another example: departing at 14:45 and arriving at 17:10 gives 2 hours 25 minutes; count 14:45 to 16:45 as a full 2 hours first, then add the 25 minutes — hard to get wrong.
6. Block 6: Two Places DistanceExample: a car travels from A towards B at 60 km/h; after 2 hours it is still 30 km from B. The distance covered = 60 × 2 = 120 km, so the distance from A to B = 120 + 30 = 150 km. In such questions add what has been covered to what remains, keeping the two parts clear. Check: covering 150 km at 60 km/h takes 2.5 hours; in 2 hours the car travels 60 × 2 = 120 km, leaving 150 - 120 = 30 km, matching the question exactly.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Distance = speed × time
• Time = distance ÷ speed
• 0.5 hour = 30 min
• Arrival = departure + travel time
• Add remaining distance