Question 1066537
.
Sagar and Akash ran 2km race twice. Akash  completed first round two minutes earlier than Sagar.
Then in second  round Sagar increased speed by 2km/hr; then Sagar finished the round 2 min. earlier than Akash.
Find their speed of running in the first round
~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
Let  a = Acash speed in the first round (in km/min),
     s = Sagar speed in the first round.

We have 

{{{2/s - 2/a}}} = 2        minutes   (first round)     (1)

{{{2/a - 2/(s+2)}}} = 2     minutes   (second round)    (2)


Add the two equations (1) and (2)  (both sides).  You will get

{{{2/s - 2/(s+2)}}} = 4.

Solve this equation for "s". For it, multiply both sides by s*(s+2). You will get

2*(s+2) - 2s = 4s*(s+2).

2s + 4 -2s = 4s^2 + 8s,

4s^2 + 8s - 4 = 0,

s^2 + 2s - 1 = 0,

{{{s[1,2]}}} = {{{(-2 +- sqrt(4 + 4))/2}}} = {{{-1 +- sqrt(2)}}}.

Only positive root works:  s = {{{sqrt(2) -1}}} km/min.  

It is the speed of Sagar in the first round.

Then the speed of Acash was a = {{{sqrt(2) + 1}}} km/min in the first round.
</pre>

Solved.