Question

Solve the linear equation: Sagar and Akash ran a 2km race twice. Akash completed the first round 2 minutes earlier than Sagar. In the second round Sagar increased his speed by 2 km/hr and Akash reduced his speed by 2 km/hr. Sagar finished 2 minutes earlier than Akash. Find their speeds of running in the first round.

Answer 1

let the speed of Sagar is vs and that of Akash is Va
time taken by Sagar to complete the race
ts=d/v
ts=2/Vs hr
and time taken by Akash is ta=2/Va hr
according to first race
ts-ta=(2/60) hr
(2/Vs)-(2/Va)=1/30. equation (1)

according to second race
ta-ts=(2/60)
[2/(Va-2)]-[2/(Vs+2)]=1/30. equation (2)
equation (1)/(2)
[1/Vs-1/Va]/[1/(Va-2)-1/(Vs+2)]=1
1/Vs-1/Va=1/(Va-2)-1/(Vs+2)
wait a sec