Difficulty: Hard
Correct Answer: 75 km/h, 100 km/h
Explanation:
Introduction / Context:
Two travelers start from the same origin at different times. A landmark (Nottingham) is reached by the later traveler in 1 hour and was passed by the earlier traveler 40 minutes earlier. This fixes a speed ratio; combining with the 1-hour start gap gives absolute speeds that also make sense over the full 300 km.
Given Data / Assumptions:
Concept / Approach:
Let V_m, V_p be speeds. Nottingham distance d_N satisfies V_p * 1 = V_m * (4/3) because Maradona took 4/3 h to reach Nottingham (from 8:24 to 9:44). Hence V_p / V_m = 4/3. Use the 1-hour start-gap arrival alignment to select the consistent pair from options.
Step-by-Step Solution:
Ratio from Nottingham condition: V_m : V_p = 3 : 4.Option (75, 100) and (60, 80) fit the 3:4 ratio.Check same-arrival feasibility over 300 km with a 1-hour delayed start: 300/75 − 300/100 = 4 − 3 = 1 h → works for (75, 100); not for (60, 80), which yields 1.25 h.
Verification / Alternative check:
Nottingham distance at (75, 100): 100*1 = 100 km; 75*(4/3) = 100 km, consistent.
Why Other Options Are Wrong:
They either break the 3:4 ratio or fail the 1-hour start-gap arrival consistency.
Common Pitfalls:
Ignoring the 40-minute offset or assuming equal arrival times without checking the start-gap consistency.
Final Answer:
75 km/h, 100 km/h
Discussion & Comments