Two cars 700 km apart at 9 am — one 1 h stop: Cars X and Y start from A and B, which are 700 km apart, at 9:00 am. Both run at 60 km/h. Car X stops from 10:00–11:00 am; car Y runs continuously. When do they meet?

Difficulty: Easy

Correct Answer: 3 : 20 pm

Explanation:


Introduction / Context:
We combine piecewise motion (one-hour halt) with relative speed to find the meeting time.


Given Data / Assumptions:

  • Initial separation = 700 km
  • Both speeds = 60 km/h
  • X stops 10:00–11:00 am; Y continues uninterrupted.


Concept / Approach:
Advance the timeline: first hour both move, next hour only Y moves, then both move again. Compute the remaining separation before the last phase and divide by relative speed.


Step-by-Step Solution:

9–10 am: both move ⇒ closing = 60 + 60 = 120 km ⇒ remaining = 700 − 120 = 580 km10–11 am: only Y moves ⇒ closes 60 km ⇒ remaining = 520 kmAfter 11 am: both move ⇒ relative speed = 120 km/h ⇒ time = 520 / 120 = 4 h 20 minMeeting time = 11:00 am + 4 h 20 min = 3:20 pm


Verification / Alternative check:
Distances from A at meeting: X moved 1 h + 4 h 20 min = 5 h 20 min of motion ⇒ 320 km; Y moved 6 h 20 min ⇒ 380 km; sum = 700 km.


Why Other Options Are Wrong:
They correspond to incorrect handling of the one-hour halt or miscomputed relative time.


Common Pitfalls:
Subtracting 60 km twice or forgetting the continuous motion of Y during the stop.


Final Answer:
3 : 20 pm

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