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Anna, Bob and Carol ran a 1000m race and each ran at a (different) constant speed throughout the entire race. When Anna finished, Bob and Carol were at the 800m and 600m mark respectively. When Bob finished, how far (in metres) was Bob ahead of Carol?

 #1
avatar+300 
+2

Let's say Anna finished in 1000 seconds (1 meter per second). Therefore, she finished in 1000 seconds.

 

Bob's speed is 80% of Anna's, as he had run 80% of the distance Anna did in the same amount of time. Therefore, his speed is 0.8 meters per second.

 

Using the same logic, Carol's speed is 0.6 meters per second.

 

Bob must've finished in 1000 / 0.8 = 1250 seconds. 


Going back to Carol. From the beginning of the race to when Bob finished (after 1250 seconds), Carol must have gone 0.6 m * 1250 sec = 750 meters, behind Bob by 1000 - 750 = 250 m.

 

So, Carol was behind Bob by 250 m when he finished :D

 May 1, 2020
 #2
avatar+657 
+1

I got the same answer. 

LuckyDucky  May 1, 2020
 #3
avatar+111329 
+3

Thanks, CentsLord and LuckyDucky   !!!

 

Here's my approach  :

 

Bob has finished   (8/10) = 4/5 of the race  and Carol has finished (6/10) =3/5  of the race when Anna finishes

 

So....in 4/5  of the race  he has as 200 meter lead on Carol

 

So...in each (1/5) of the race  he gains 200 /4  = 50 meters on Carol

 

So....for the last 1/5  of the race he picks up another 50m on Carol

 

So....when he crosses the finish line, he is  200 + 50  =  250 m  ahead of Carol

 

 

cool cool cool

 May 1, 2020
 #4
avatar+657 
+2

Cool! it's always interesting to have multiple ways to solve a question.

LuckyDucky  May 1, 2020

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