D-12MathsSat 29 Aug

Speed, distance, time

Average speed traps under time pressure.

Speed, distance and time are one family. If you know two, you can find the third — but only if the units match (hours with km/h, not minutes mixed in by accident). Average speed is total distance over total time, not the average of the two speeds.

Picture it: cover what you want to find

D = S × T

Cover D

S = D ÷ T

Cover S

T = D ÷ S

Cover T

Remember — units first

Write what you know, with units (km, miles, hours, minutes).
Convert so they match: 30 minutes = 0.5 hours; 90 minutes = 1.5 hours.
Cover the letter you want on the triangle and calculate.
Ask: is this a sensible speed for a car / walker / train?

Exam trap

Averaging the two speeds. Going 60 km/h for 1 hour then 40 km/h for 1 hour is not “50 km/h average” if the times differ — and even with equal times, check you are not mixing a faster short burst with a long crawl.

✗ (60 + 40) ÷ 2 = 50

Only works if the times are equal — and still check

✓ Total km ÷ total hours

Always safe for average speed

Question patterns you might see

Same triangle. Watch the time unit.

1 · Simple — Find the speed
“A bus travels 90 km in 2 hours. What is its average speed?”
D
90 km
→
T
2 h
→
S
45 km/h
Speed = 90 ÷ 2 = 45 km/h
2 · Simple — Find the time
120 km at 40 km/h → T = 120 ÷ 40 = 3 hours. If the answer options are in minutes, × 60 → 180 minutes.
D
120 km
→
S
40 km/h
→
T
3 h = 180 min
3 · Medium — Minutes mixed with hours
“Sam cycles 18 km in 40 minutes. Speed in km/h?”
1. 140 minutes = 40 ÷ 60 = 2/3 hour.
2. 2Speed = 18 ÷ (2/3) = 18 × 3/2 = 27 km/h.
3. 3Or scale up: in 40 min he does 18 km, so in 60 min he does 18 × 1.5 = 27 km.
27 km/h
4 · Medium — Two-part journey
Total distance 100 km, total time 2 h → average speed 50 km/h. (Here the times were equal, so the naive average matches — still use totals so the habit sticks.)
5 · Trickier — Same distance, different speeds
60 km at 60 km/h (1 hour) then 60 km at 30 km/h (2 hours). Total 120 km in 3 hours → average 40 km/h, not 45. More time was spent at the slower speed.
Distance
120 km
→
Time
3 h
→
Average
40 km/h
6 · Trickiest — Leave at x, arrive at y
Leaves at 09:40, arrives at 11:10, travels 60 km. Time = 1 hour 30 minutes = 1.5 h. Speed = 60 ÷ 1.5 = 40 km/h. Count the minutes on a clock line; don’t subtract the times as if they were decimals (11.10 − 9.40 is not 1.70 hours).

Coach tip: scribble D, S, T in a triangle in the margin on every speed question. Cover the one you need.

Tomorrow (D-11): synonyms that aren’t antonyms.

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