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Question 7 : A straight road connects points A and B. Car 1 travels from A to B and Car 2 travels from B to A, both leaving at the same time. After meeting each other, they take 45 minutes and 20 minutes, respectively, to complete their journeys. If Car 1 travels at the speed of 60 km/hr, then the speed of Car 2, in km/hr, is

  1. 90
  2. 80
  3. 70
  4. 100

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Explanatory Answer

Let the meeting point be D. Let’s assume C1 takes t minutes to reach the meeting point. Then C2 takes same t minutes to reach the meeting point. Graphs showing translations of mod of x After reaching the destinations...
C1 takes t minutes to cover AD, while C2 takes 20 minutes
C1 takes 45 minutes to cover DB, while C2 takes t minutes

the ratio of speeds of C1 and C2 on the stretch AD will be equal to the ratio of their speed on the stretch DB.
When the distances are the same, the ratio of speeds is the inverse ratio of time taken.
ratio of speeds of C1 and C2 on the stretch AD = \\frac{20}{t})
ratio of speeds of C1 and C2 on the stretch DB = \\frac{t}{45})
Therefore, \\frac{20}{t}) = \\frac{t}{45})
t × t = 45 × 20
t 2 = 900
t = 30.

\\frac{Speed of C1}{Speed of C2}) = \\frac{20}{t})
\\frac{60}{Speed of C2}) = \\frac{20}{30})
Speed of C2 = 90 kmph

The answer is, "90"

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