What you’ll learn
Compare quantities using unit rates.
Key idea
Divide each distance by its own time to put both runners on a one-hour basis.
Pair each distance with its own time; raw totals and swapped denominators cannot justify the requested comparison.
Worked example
Classify examples and non-examples for the concept 'Compare quantities using unit rates'.
Runner A covers 6 km in 3 h; Runner B covers 8 km in 2 h. Is 'A has the greater speed' valid? Classify with comparable unit-rate evidence.
- A's rate is 6÷3=2 km/h; B's is 8÷2=4 km/h.
- Compare the rates in the same units; B is faster.
Answer: Invalid — A runs 2 km/h and B runs 4 km/h, so B has the greater speed.
Quick Check
Classify examples and non-examples for the concept 'Compare quantities using unit rates'.
Runner A covers 6 km in 3 h; Runner B covers 24 km in 4 h. Is 'A has the greater speed' valid? Classify with comparable unit-rate evidence.