A reliable method
Calculate total distance divided by total time. For pursuit, divide the initial gap by the difference in speeds, using consistent units throughout.
The common trap
The arithmetic mean of two speeds works for equal times, but usually fails for equal distances. A catch-up time begins when the pursuer starts if the gap is measured then.
Check the conclusion
Draw a simple timeline and label the gap at the start. Substitute the final time into both positions and verify that they coincide.
Contrast the cases
Equal one-hour journeys at 30 and 60 km/h cover 90 km in two hours, averaging 45. Equal 60-km distances at the same speeds instead take three hours and average 40. The data determine the weighting. In pursuit, a car at 42 km/h following a van at 30 km/h closes a 24-km gap in 2 hours because relative speed is 12, not their sum.
Transfer and explain
Transfer: two vehicles move in opposite directions at 30 and 42 km/h. Their separation grows by 72 km each hour. Compare with same-direction pursuit to explain why the sign of the rate combination changes.
A vehicle travels for 2 hours at 33 km/h and 3 hours at 53 km/h. What is its average speed, in km/h?
- Total distance is 2(33) + 3(53) = 225 km.
- Total time is 5 hours.
- Average speed is 45 km/h.
Compare the other answer choices
Averages speeds despite unequal travel times.
Divides total distance by only the second time.
Returns total distance instead of average speed.
Divides total distance by only the first time.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
GMAT exam contentSiyavula Grade 10 mathematics foundation reference