Question
During the first 90 km of his trip, 'X' drove at a speed
of 60 km/h. In the next 150 km, he increased his speed by 'y%' compared to his initial speed. For the remaining 20% of the total journey, he drove at a speed of 120 km/h. If the average speed for the entire trip was recorded as 75 km/h, determine the value of 'y'.Solution
Average speed = (Total distance covered/Total time taken) Total distance covered by 'X' = (90 + 150) ÷ 0.8 = 300 km Let the speed of 'X' at which he travelled for 150 km be 'a' km/h Total time taken by 'X' to complete the journey = (90/60) + (150/a) + (60/120) = 1.5 + (150/a) + 0.5 = {2 + (150/a)} hours Also, total time taken = (300/75) = 4 hours Therefore, 2 + (150/a) = 4 Or, 'a' = (150/2) = 75 So, percentage increase in the speed = {(75 - 60)/60} X 100 = 25% So, y = 25
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