Rakesh and Saket run a race of 2 km. First Rakesh gives Saket a start of 200 meters and beats him by 1 minute. If Rakesh gives Saket a start of 6 minutes Rakesh is beaten by 1 km. Find the time in minutes in which Rakesh and Saket can run the races separately.
Answers
Given : Rakesh and Saket run a race of 2 km.
First Rakesh gives Saket a start of 200 meters and beats him by 1 minute.
If Rakesh gives Saket a start of 6 minutes Rakesh is beaten by 1 km.
To Find : the time in minutes in which Rakesh and Saket can run the races separately.
Solution:
Rakesh and Saket run a race of 2 km = 2000 m
Rakesh gives Saket a start of 200 meters and beats him by 1 minute.
=> Time taken by Rakesh = T mins
Then time taken by saket for 2000 - 200 = 1800 m = T + 1 Mins
Speed of rakesh = 2/T
Speed of saket = 1.8/(T + 1)
Rakesh gives Saket a start of 6 minutes Rakesh is beaten by 1 km
Time taken by rakesh to complete = 2 - 1 = 1 km
= 1/(2/T)
= T/2 mins
Time taken by saket = T/2 + 6 mins
{1.8/(T + 1)} {T/2 + 6} = 2
=> 1.8(T + 12) = 4(T + 1)
=>1.8T + 21.6 = 4T + 4
=> 2.2T = 17.6
=> T = 8
time in minutes in which Rakesh races = 8 Min
Speed of saket = 1.8/(T + 1) = 1.8/(8 + 1) = 0.2 km/min
=> Time taken by saket = 2/0.2 = 10 min
Rakesh finish in 8 Mins
Saket finished in 10 mins
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