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CBSE Class 9 Answered

A person being chased by a lion is running on a straight line towards his car
at a constant speed of 4m/s. The car is at a distance of d meters away from
the person. The lion is 26 m behind the person and running at a constant
speed of 6 m/s. The person reaches the car safely. What is the maximum
possible value of d?
Asked by Atal Kumar | 16 May, 2015, 04:02: AM
answered-by-expert Expert Answer
In order for the lion to catch the person over the distance d, the lion must reach the car at the same time as that of the person.
In the time t taken by the man to reach the car, the lion must travel a total distance of d + 26 m.
For the person:
begin mathsize 12px style straight nu subscript man space end subscript equals space straight d over straight t space Or comma space straight t space equals space straight d over straight nu subscript man space end subscript space equals space straight d over 4 end style
For the lion:
begin mathsize 12px style straight nu subscript lion space end subscript equals space straight d over straight t space Or comma space straight t space equals space straight d over straight nu subscript lion space end subscript equals space fraction numerator straight d space plus space 26 over denominator 6 end fraction end style
Since the man and the lion runs for the same time, we have
begin mathsize 12px style space straight d over 4 equals fraction numerator straight d space plus space 26 over denominator 6 end fraction end style
6d = 4d + 104
d = 52 m
Thus, the maximum possible distance distance is 52 m.
Answered by Yashvanti Jain | 13 Dec, 2017, 06:34: PM

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