The Lion is Hungry!

A person being chased by a lion is running in a straight line towards his car at a constant speed of 4 4 m s 1 ms^{-1} .The car is at a distance of d \mathcal {d} metres away from the person. The lion is 26 26 m \text {m} behind the person and running at a constant speed of 6 6 ms 1 \text{ms}^{-1} . The person reaches the car safely . What is the maximum possible value of d \mathcal {d} in metres ?

Note: Suppose that the person takes no time to sit in the car.


The answer is 52.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Sabhrant Sachan
Jun 9, 2016

To find the maximum distance/displacement, Time taken by the Lion and the person to reach the car must be equal t Lion = t Person d 4 = d + 26 6 3 d = 52 + 2 d d = 52 m \text{To find the maximum distance/displacement, Time taken by the Lion and the person to reach the car must be equal} \\ t_{\text{Lion}}=t_{\text{Person}} \implies \dfrac{d}{4}=\dfrac{d+26}{6} \\ 3d=52+2d \implies \color{royalblue}{\boxed{d=52 m}}


NOTE: Please Mention that we to submit our answer in meters \text{NOTE: Please Mention that we to submit our answer in meters }

Thanks ! Edited.

Rishabh Tiwari - 5 years ago

I solved in the same way! Nice!

Victor Paes Plinio - 5 years ago

Nice solution ,+1!

Rishabh Tiwari - 5 years ago

nice one (+1) !

Abhay Tiwari - 5 years ago
Abhay Tiwari
Jun 9, 2016

Man's speed = 4 m s 1 4 \space ms^{-1} , Lion's speed = 6 m s 1 6 \space ms^{-1}

Relative speed = 6 4 = 2 m s 1 6-4=2\space ms^{-1}

Which means that lion is gaining 2 meters every second. Following this, after 13 seconds he will be eaten alive. He better reach his car in 13 seconds.

Maximum distance the man can run in 13 seconds= 13 s e c o n d s × 4 m s 1 = 52 13 \space seconds \space × \space 4 \space ms^{-1}=\color{magenta}{\boxed{52}}

Another interesting approach, +1!

Rishabh Tiwari - 5 years ago

Log in to reply

Thanks a lot ;).

Abhay Tiwari - 5 years ago

a better solution..+1!

Sabhrant Sachan - 5 years ago
Rishabh Tiwari
Jun 9, 2016

Consider a time 't' after which the man covers the distance 'd' ; Now since the speed of the man is 4m/s & that of lion is 6m\s , Therefore we can write \longrightarrow

d = 4 t d=4t .......... ( 1 ) (1) &

26 26 + + d d = = 6 t 6t ........ ( 2 ) (2)

Solving these two equations, we get t t = 13 =13 , Putting this value of t t in the second equation we get our answer as d = 52 m \boxed {d=52m} .

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...