A car travels 280 miles in 5 hours. What is its average speed in miles per hour?

The car's average speed equals 56 miles per hour when the total distance traveled of 280 miles is divided by the elapsed time of 5 hours according to the fundamental speed formula (speed = distance ÷ time), yielding the quotient 56 that represents the constant rate required to cover the distance in the specified duration.

A. 52 mph

This speed would cover only 260 miles in 5 hours (52 × 5 = 260), falling 20 miles short of the actual 280-mile journey. This error likely originates from miscalculating 280 ÷ 5 through faulty decomposition: incorrectly computing 250 ÷ 5 = 50 then adding 2 instead of 6 for the remaining 30 miles (since 30 ÷ 5 = 6), yielding 50 + 2 = 52. Another plausible pathway involves transposing digits in the dividend (reading 280 as 260) then correctly calculating 260 ÷ 5 = 52. The 4-mph deficit represents exactly 20 miles of unaccounted distance over the 5-hour period highlighting how minor computational errors in division produce meaningful discrepancies in rate calculations with practical consequences for travel planning, fuel estimation, and scheduling accuracy where speed miscalculations cascade into significant time or distance prediction errors.

B. 54 mph

This rate would cover 270 miles in 5 hours (54 × 5 = 270), still 10 miles short of the actual distance. The error pattern suggests approximation rather than precise calculation possibly rounding 280 down to 270 before division (270 ÷ 5 = 54) or executing 280 ÷ 5 = 56 correctly then erroneously subtracting 2 during transcription. Another plausible origin involves confusing the problem with a similar scenario where distance equals 270 miles. The 2-mph deficit (approximately 3.6% error) represents a moderate miscalculation that might escape detection in casual estimation but proves significant in contexts requiring precision such as aviation navigation, athletic pacing, or delivery logistics where consistent speed deviations accumulate into substantial schedule disruptions over extended durations. This distractor effectively identifies students who prioritize computational speed over accuracy or who lack confidence in mental division with non-round dividends.

C. 56 mph

This value correctly represents the average speed through multiple verification approaches demonstrating computational fluency and conceptual understanding. Direct division: 280 ÷ 5 = 56. Multiplicative verification: 56 mph × 5 hours = 280 miles, confirming distance reconstruction. Decomposition method: 280 = 250 + 30; 250 ÷ 5 = 50; 30 ÷ 5 = 6; 50 + 6 = 56. Fraction simplification: 280/5 = 56/1 = 56. Unit analysis confirmation: miles ÷ hours = miles per hour, validating dimensional appropriateness. This solution demonstrates mastery of rate concepts including formula application (r = d/t), inverse relationship understanding (distance = rate × time for verification), computational flexibility with division, and dimensional awareness integrated competencies essential for physics problem-solving, travel planning, athletic performance analysis, and transportation logistics where accurate speed determination informs scheduling, fuel consumption estimates, and safety calculations. The integer quotient reflects appropriate problem design where distance is deliberately selected as a multiple of time to yield whole-number speed, building foundational rate comprehension before introducing fractional results that add computational complexity.

D. 60 mph

This speed would cover 300 miles in 5 hours (60 × 5 = 300), exceeding the actual distance by 20 miles. This error likely originates from rounding 280 up to 300 before division (300 ÷ 5 = 60) a mental shortcut prioritizing computational convenience over precision. Students might recognize that 300 ÷ 5 = 60 easily but fail to adjust downward for the 20-mile difference (20 ÷ 5 = 4 adjustment needed: 60 - 4 = 56). Another plausible pathway involves misreading 280 as 300 through digit substitution or visual scanning error. The 4-mph excess mirrors option A's deficit symmetrically around the correct value, revealing how rounding errors often manifest as bidirectional approximations bracketing the accurate result. This distractor proves particularly effective at identifying students who employ estimation strategies in contexts requiring exact calculation a critical distinction as real-world navigation, legal speed compliance, and scientific measurement demand precision where even 4-mph deviations carry meaningful consequences for safety, legality, or experimental validity.

Conclusion

The 56 mph average speed emerges through precise application of the rate formula validated through multiplicative reconstruction and multiple computational pathways ensuring result integrity. This problem reinforces foundational quantitative reasoning competencies essential across scientific and practical domains: understanding rate as a derived quantity representing distance covered per unit time, executing division with multi-digit dividends, recognizing the inverse relationship between rate and time for fixed distances, and maintaining dimensional consistency throughout calculations. Mastery of these integrated skills proves indispensable for physics (velocity calculations), transportation (trip planning, fuel efficiency), sports science (pace analysis), and logistics (delivery scheduling) where speed miscalculations produce cascading errors in time estimation, resource allocation, and safety margins. The symmetric rounding errors at 52 and 60 mph highlight a persistent challenge in quantitative literacy: distinguishing contexts requiring estimation from those demanding exact calculation a metacognitive skill requiring explicit development through varied problem presentations that specify precision requirements while building computational fluency with both mental approximation and exact algorithms.