Aptitude:speed and distance [Section 1 of 1] Q3 of 30 Marks 1 General Instructions 100% ×CloseTest time left: 21:02Select the correct answerTwo cars A and B travel from one city to another city, at speeds of 60 km/hr and 108 km/hour respectively. If car B takes 2 hours lesser time than car A for the journey, then what is the distance (in km) between the two cities?
Question
Aptitude:speed and distance [Section 1 of 1] Q3 of 30 Marks 1 General Instructions 100% ×CloseTest time left: 21:02Select the correct answerTwo cars A and B travel from one city to another city, at speeds of 60 km/hr and 108 km/hour respectively. If car B takes 2 hours lesser time than car A for the journey, then what is the distance (in km) between the two cities?
Solution
Let's denote the distance between the two cities as D (in km), the speed of car A as Sa (in km/hr), the speed of car B as Sb (in km/hr), and the time difference as Δt (in hours).
From the problem, we know that:
Sa = 60 km/hr Sb = 108 km/hr Δt = 2 hours
We also know that the time it takes for each car to travel from one city to another is equal to the distance divided by the speed. Therefore, we can write the following two equations:
Ta = D/Sa Tb = D/Sb
Since car B takes 2 hours less than car A to travel the same distance, we can write:
Ta = Tb + Δt
Substituting the expressions for Ta and Tb from the first two equations into this equation gives:
D/Sa = D/Sb + Δt
Solving this equation for D gives:
D = Sa * Sb * Δt / (Sa - Sb)
Substituting the known values gives:
D = 60 km/hr * 108 km/hr * 2 hours / (60 km/hr - 108 km/hr)
Solving this equation gives:
D = 216 km
Therefore, the distance between the two cities is 216 km.
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