Question
P and Q each had designated spots
to set up their temporary shops. The distance from their house (they live in the same house) to P’s shop was 32 km, and to Q’s shop was 40 km. They usually left home at the same time and arrived at their respective shops by 8:00 a.m. One day, their shop locations were swapped. On that day, P left home 16 minutes earlier than Q so that he could reach his new spot on time. Find P’s speed.Solution
ATQ,
P and Q travel distances of 32 km and 40 km respectively. They both reach their destinations at the same time. Thus, their speed ratio is 32:40, which simplifies to 4:5. Assume P’s speed is 4x km/h and Q’s speed is 5x km/h. On the interchange day: Time taken by P to travel to Q’s place = 40 / (4x) hours Time taken by Q to travel to P’s place = 32 / (5x) hours According to the question: (40 / 4x) – (32 / 5x) = 16/60 Solving gives x = 13.5. Therefore, P’s speed = 4x = 54 km/h.
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