Question
Amit has two routes, βXβ and
βYβ, to travel from his home to his gym. The length of route βXβ exceeds the length of route βYβ by 15 km. On Monday, Amit chose route βXβ. He traveled at a certain speed for 2 hours, then increased his speed by 20% for the rest of the journey. On Tuesday, he opted for route βYβ. For the first 2 hours, he traveled at a speed that was 20% less than his initial speed on Monday, and then increased his speed by 25% for the remainder of the journey. If Amit completed both routes in exactly 3 hours, determine the distance of the longer route.Solution
ATQ,
For route βXβ: Let the speed of Amit for 2 hours be βaβ km/hr Therefore, total distance covered = 2a + 1.2a = 3.2a km For route βYβ: Speed of Amit for 2 hours = 0.8a km/hr Therefore, total distance covered = 0.8a Γ 2 + 1.25 Γ 0.8a = 2.6a km According to the question, 3.2a β 2.6a = 15 Or, a = 15/0.6 = 25 Therefore, distance of the longer route = 3.2a = 80 km
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