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 speed of Sagar is P km/h
speed of Akash is Q km/h
and distance of path where they run is 2 km

A/C to question,
time taken by Sagar = time taken by Akash + 2 min
2/P = 2/Q + 2/60 [ in hour ]
2/P - 2/Q = 1/30 -----------------(1)

again,
speed of Sagar = (P + 2) km/h
speed of Akash = (Q - 2) km/h

time taken by Akash = time taken by Sagar - 2min
2/(P + 2) = 2/(Q -2) - 2/60
2/(Q - 2) - 2/(P + 2) = 1/30 ------(2)

solve equations (1) and (2)
P = 10 km/h
Q = 12 km/h

hence, speed of Sagar = 10 km/h
speed of Akash = 12 km/h