Question
A car's speed is 20% faster than that of a bike. The car
takes 30 minutes longer than the bike to cover 120 km, while the bike covers 80 km. Find the time it takes for an auto rickshaw to travel 154 km, knowing that its speed is the average of the speeds of the car and the bike.Solution
Let the speed of bike be 'v' km/h. Speed of car = '1.2v' km/h So, (120/1.2v) - (80/v) = (30/60) Or, (100/v) - (80/v) = (1/2) Or, (20/v) = (1/2) Or, 'v' = 40 Speed of auto = (v + 1.2v) ÷ 2 = 1.1v = 1.1 X 40 = 44 km/h Therefore, required time = (154/44) = 3.5 hours = 3.5 X 60 = 210 minutesÂ
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