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Airline flight scheduling between two cities

CAT 2007 Slot 1 · Quantitative Ability · Medium · Time Speed Distance

This is a medium Quantitative Ability question set from the CAT 2007 Slot 1 paper. It tests Time Speed Distance. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Passage / data set

Cities A and B are in different time zones. A is located 3000 km east of B. The table below describes the schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on the same day.

Departure CityDeparture TimeArrival CityArrival Time
B8:00 amA3:00 pm
A4:00 pmB8:00 pm

Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind blowing from east to west at 50 km per hour.

Question 1 of 2

What is the time difference between A and B?

  1. A.

    1 hour and 30 minutes

  2. B.

    2 hours

  3. C.

    2 hours and 30 minutes

  4. D.

    1 hour

  5. E.

    Cannot be determined

Answer

D

Explanation

Let yy be cruising speed and xx be time difference in hours. Flight B to A: travel time is (7−x)(7 - x) hours, speed is y−50y - 50. Flight A to B: travel time is (4+x)(4 + x) hours, speed is y+50y + 50. Solving (7−x)(y−50)=3000(7 - x)(y - 50) = 3000 and (4+x)(y+50)=3000(4 + x)(y + 50) = 3000 yields x=1x = 1 hour and y=550y = 550 km/hr.

Question 2 of 2

What is the plane's cruising speed in km per hour?

  1. A.

    700

  2. B.

    550

  3. C.

    600

  4. D.

    500

  5. E.

    Cannot be determined

Answer

B

Explanation

Cruising speed y=550y = 550 km/hr.

Why the other options are wrong

  • A.700 — does not satisfy the condition asked in this question, so it is not the correct answer.
  • B.550 — does not satisfy the condition asked in this question, so it is not the correct answer.
  • C.600 — does not satisfy the condition asked in this question, so it is not the correct answer.
  • D.500 — does not satisfy the condition asked in this question, so it is not the correct answer.
  • E.Cannot be determined — does not satisfy the condition asked in this question, so it is not the correct answer.

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