{"id":11220,"date":"2022-06-28T18:59:47","date_gmt":"2022-06-28T13:29:47","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11220"},"modified":"2022-06-28T19:00:31","modified_gmt":"2022-06-28T13:30:31","slug":"a-train-covered-a-certain-distance-at-a-uniform-speed-if-the-train-would-have-been-10-km-hr-faster-it-would-have-taken-2-hours-less-than-the-scheduled-time-and-if-the-train-were-slower-by-10-km-hr","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/a-train-covered-a-certain-distance-at-a-uniform-speed-if-the-train-would-have-been-10-km-hr-faster-it-would-have-taken-2-hours-less-than-the-scheduled-time-and-if-the-train-were-slower-by-10-km-hr\/","title":{"rendered":"A train covered a certain distance at a uniform speed. If the train would have been 10 km\/hr faster, it would have taken 2 hours less than the scheduled time. And if the train were slower by 10 km\/hr, it would have taken 3 hours more than the scheduled time. Find the distance covered by the train."},"content":{"rendered":"
Let x km\/hr\u00a0 be the original speed of the train and y hrs be the time taken by the train to complete the journey.<\/p>\n
Then, Distance covered = xy km<\/p>\n
Case 1<\/strong> : When\u00a0 speed = (x + 10) km\/hr<\/p>\n time taken = (y – 2) hr<\/p>\n Distance = (x + 10) (y – 2)<\/p>\n xy = (x + 10) (y – 2)<\/p>\n \\(\\implies\\) 2x – 10y + 20 = 0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0……….(1)<\/p>\n Case 2<\/strong> : When speed = (x – 10) km\/hr<\/p>\n time taken = (y + 3) hr<\/p>\n Distance = (x – 10)(y + 3)<\/p>\n xy = (x – 10)(y + 3)<\/p>\n \\(\\implies\\) 3x – 10y – 30 = 0\u00a0 \u00a0 \u00a0 \u00a0…….(2)<\/p>\n Now, subtract equation (1) from (2), we get<\/p>\n x – 50 = 0\u00a0 \u00a0 \u00a0\\(\\implies\\)\u00a0 \u00a0 \u00a0 x = 50<\/p>\n Put the value of x = 50\u00a0 in equation (1), we get<\/p>\n 100 – 10y + 20 = 0\u00a0 \u00a0 \u00a0 \u00a0\\(\\implies\\)\u00a0 \u00a0y = 12<\/p>\n Hence, the distance covered by train is \\(12\\times 50\\) = 600 km<\/strong><\/p>\n\n\n <\/p>\n","protected":false},"excerpt":{"rendered":" Solution : Let x km\/hr\u00a0 be the original speed of the train and y hrs be the time taken by the train to complete the journey. Then, Distance covered = xy km Case 1 : When\u00a0 speed = (x + 10) km\/hr time taken = (y – 2) hr Distance = (x + 10) (y …<\/p>\n