Den Bosch and Eastbourne are 300 km apart. Maradona leaves Den Bosch at 8:24 a.m.; Pele leaves an hour later from the same place. After 1 hour of travel, Pele reaches Nottingham, which Maradona passed 40 minutes earlier. Find their speeds (Maradona, Pele).

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:

  • Pele reaches Nottingham 1 hour after starting.
  • Maradona passed Nottingham 40 minutes earlier than that.
  • Both depart Den Bosch; route passes Nottingham en route to Eastbourne (300 km).


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

More Questions from Time and Distance

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion