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Q: There was a 2 kilometre race between a cheetah and an elephant. Soon after the start of the race, the cheetah took a huge lead. On realizing that even after taking a nap of ‘t’ min, he would beat the elephant by 13 min, he stooped under a tree and went to sleep. Meanwhile the elephant kept walking. When the cheetah woke up, he realized that he had slept for (14 + t) min, and immediately started running towards the target at a speed 1.5 times his original speed. The race eventually ended in a dead heat. If the ratio of the original speed of the cheetah to that of the elephant was 6 : 1 and the cheetah overstretched his nap by 7/6*t min, then how long (in minutes) did the elephant take to complete the race?
Satish Shingrakhiya - Sep 1, 2023
cheetah overstretched by 14 mins = 7t/6 => t = 12 minutes => at original speed cheetah can beat elephant by t + 13 = 25 minutes.
Let Time taken by cheetah = tc => time taken by elephant = tc + 25
Now distance is const => Se/Sc = (tc + 25)/tc = 6/1 => tc = 5 minutes
=> time taken by elephant = 30 minutes
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