Total Distance of the Race?

A runs 8/3 times as fast as B. A gives B a start of 80 meters. 

If both finish the race at the same time, what was the total distance of the race?

Here is the TOTAL DISTANCE of Race!

      

                           

Total Distance of the Race!

 

What was the PUZZLE?

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Suppose B’s speed is 1 m/s, then A’s speed will be 8/3 m/s.

A allowed B to go 80 meters ahead, meaning the distance between them is 80 meters.

Now, after A starts running, every second B increases this distance (80 m) by 1 meter, but A (because his speed is higher) reduces this distance by 8/3 meters.
So, each second the distance between them decreases by:

8/3 − 1 = 5/3 meters per second.

This means that to close the 80-meter gap, the time required is:

80 ÷ (5/3) = 48 seconds.

Both finish the race at the same time, meaning the gap becomes zero at the finish line, and from A’s perspective, it took him 48 seconds to complete the race at a speed of 8/3 m/s.

Therefore, the total race distance must be:

(8/3) × 48 = 128 meters.

Or

B run for 48 seconds at speed of 1m/s means covered distance of 48m. Since he started 80m ahead of A the total distance of race is 80 + 48 = 128m.

                                                    

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100m Running Race

Lavesh, Bolt, and Lewis race each other in a 100 meters race. All of them run at a constant speed throughout the race.

Lavesh beats Bolt by 20 meters.
Bolt beats Lewis by 20 meters.

How many meters does Lavesh beat Lewis by ? 

Know here the answer! 

Source 

Winner Beats Second Runner Up by...

What was the question? 

Let Lavesh's speed be 10 m/s. Then he must have taken 10 seconds to finish the race. Since Bolt was beaten by Lavesh by 20 m he must have run 80m when Lavesh finished race in 10 seconds (t=10). So his speed would be 8 m/s.

Now Bolt requires 100/0.8 = 12.5 seconds to finish the race. When he finished, Lewis was 20m behind i.e. 80m from starting point at t = 12.5. So Lewis speed is 80/12.5 = 6.4 m/s

At t = 10 seconds, when Lavesh finished his race Lewis must be at 6.4 x 10 = 64 m from starting point. Hence Lavesh beats Lewis by 100 - 64 = 36 m.

Another method.

Let L be the speed of Lavesh, B be the speed of Bolt & W be that of Lewis. Then,

L/B = 100/80 = 5/4

L = (5/4) B  .......(1)

Similarly,

B/W = 100/80 = 5/4

B = (5/4) W .......(2)

Putting (2) into (1),

L = (5/4) x (5/4) W

L/W = 25/16

L = (25/16) W

For given time t, when Lavesh finished the race,

Distance by L/ Distance by W = 25 / 16

100 m/ Distance by W = 25 / 16

Distance by W = (16 x 100) / 25 = 64.

  
So when Lavesh finished cross line at 100 m, Lewis was at 64m i.e. 36m behind. In other words, Lavesh beats Lewis by 100 - 64 = 36 m.