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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
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Let a = Acash speed in the first round (in km/min),
s = Sagar speed in the first round.
We have
= 2 minutes (first round) (1)
= 2 minutes (second round) (2)
Add the two equations (1) and (2) (both sides). You will get
= 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,
= = .
Only positive root works: s = km/min.
It is the speed of Sagar in the first round.
Then the speed of Acash was a = km/min in the first round.
Solved.