SOLUTION: A tiger and a lion start at exactly the same place on the same road and run in the same direction. if the tiger runs 30 mph and the lion runs at only 2 mph but starts 16 hours befo

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Question 1102263: A tiger and a lion start at exactly the same place on the same road and run in the same direction. if the tiger runs 30 mph and the lion runs at only 2 mph but starts 16 hours before the tiger, how many hours will the tiger have to run before it catches the lion?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Not the only method, but 
                SPEED      TIME           DISTANCE
FAST CAT          30         d/30            d
SLOW CAT           2         d/2             d
Difference                 16

Find d, first and use for finding d%2F30.
highlight_green%28d%2F2-d%2F30=16%29
30%28d%2F2-d%2F30%29=30%2A16
15d-d=30%2A16
14d=30%2A16
7d=30%2A8
d=240%2F7
d=34.2857%2Amiles, or 34%262%2F7miles


TIME FOR THE TIGER
d%2F30

%28240%2F7%29%281%2F30%29

highlight_green%281.1429%2Ahours%29
-
1 hour 9 minutes

Answer by ikleyn(52812) About Me  (Show Source):
You can put this solution on YOUR website!
.
1 - Physics style solution 

Time to catch = %282%2A16%29%2F%2830-2%29 = 32%2F28 hours = 14%2F28 hours = 11%2F7 hours.


Explanations:


2*16 = 32 miles in the numerator is the "head start distance".

(30-2) = 28 miles per hour in the denominator is their relative speed,

         which is EXACTLY THE RATE of decreasing the distance between them.


2 - Algebra style solution 

30*t = 2*(t+16).        <<<<----====  This equation says that they cover the same distance, but for different time.


Solve for t, which is time counted after the tiger started.


After completing this simple solution you will get the same answer.


See the lessons
    - - Travel and Distance problems
    - - Travel and Distance problems for two bodies moving in opposite directions
    - - Travel and Distance problems for two bodies moving in the same direction (catching up)
in this site.


Everything is/was explained there.

You will find TONS of similar solved problems there.


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@josgarithmetic took very inadequate approach to solve the problem.

NEVER USE SUCH approach in problems like this.