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 | 16th May, 2015, 04:02: AM

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 | 13th Dec, 2017, 06:34: PM