Aptitude - Races and Games - Discussion

Let total distance is "y" mtr.
As per the question A gives B a start of 80 mtr.
So we can say that A runs "y" mtr while B covers (y-80) mtr.
Now B's speed is X m/sec (say)
And A's speed is 5X/3 m/sec
Now as they both have to reach the finish point at the same time then we can say that time taken by both the players to reach the same spot is equal.
Time taken by A = y/(5X/3) secs --> (i)
and B = (y-80)/X secs --> (ii)
Now eqating the equation i and ii we get ,
y/5X/3= (y-80)/X
3y= 5y-400
2y= 400
y= 200 m (ans.)

An alternate solution which is more general.

Let the speed of B = x.
Hence speed of A = 5/3 x.

Let the distance from B to the finish point is D.

The distance to be covered by A = 80 + D as A is 80 m behind B.

The time taken by both will be the same.

So, D/x = (80 + D)/(5x/3) => D = 120 m.

Hence the total distance from A is = 120+80 = 200m.

After every 5m A takaes a lead 2m
so as A moves forward another 5m i.e 5+5=10
the lead increase by 2.& i.e 2+2=4
there foe 15 it is 6, for 20 it is 8.
to compensate B's lead of 80,
and reach the point both a&b at the same time .
it must 200 i.e 80m lead and both will reach at the same time.

Given a is 1(2/3) as fast as b.

Ratio of their speeds a:b = 5:3.

Speed is directly proportional to distance traveled.

d1:d2 = 5:3.

Assume a travels 5 m in t time then b travels 3 m in the same time.

That's it and continue as explained in the answer.

The difference between A and B is 80m.

Let x be the total distance to cover in race.

In the problem he given A and B to reach at same time. i.e.4.

Time taken by A = time taken by B.

x/5 = (x-80)/3.

3x = 5x - 400.

2x = 400.

x = 200.

Speed of A:B = 5:3.

Time A = Time B.

Distance A/Speed A = Distance B/Speed B.

Distance A/Distance B = 5/3.

A/A+80 = 5/3.

3A = 5A+400.

2A = 400 (Neglecting negative sign as its distance).

A = 200 m.

x is B speed then A speed is 5x/3 let pole is at distance y.

Then y-80/x=t for b y/5x/3=t for a equate both you get y as 200,

Why to equate? because both should come at same time.

After every 5 m, A takes a lead of 2 m.
And B already 80 m ahead of A.

So A has to cover 80 m.
A will be take 40min to cover 80 m.

40 m*5 = 200.

In the question, its is given that A runs 1 2/3 times as fast as B.

They why the speed of A : B = 5 : 3 is taken in solution.

Hello @Shivakrishna A and B to reach at same time i.e., 4 has not mentioned in the problem see the problem clearly write.