Madhulika and rita ran a 2 km race twice. In the first round rita finishes 2 min earlier than madhulika. In the second round, madhulika increased her speed by 2 km/hr and rita reduced her speed by 2 km/hr, in the second round, madhulika finishes 2 min earlier than rita. Find the speeds of their running the first round.
Answers
Let say Madhulika Speed in First Round= M km/Hr
Let say Rita Speed in first Round = R km/Hr
Distance = 2km
Time taken by Madhulika in first round = 2/M Hr
Time taken by Ritu in first round = 2/R Hr
2/M - 2/R = 2/60 ( rita finishes two mins earlier 2min = 2/60 Hr)
=> 1/M - 1/R = 1/60
multiplying by 60RM both sides
=> 60R - 60M = RM - eq 1
in Second round
Madhulika Speed = M+2 km/Hr
Ritu speed = R-2 Km/Hr
Time taken by Madhulika = 2/(M+2) hr
Time Taken by Ritu = 2/(R-2) hr
2/(R-2) - 2/(M+2) = 2/60 ( madhulika finishes two mins earlier in second round)
=> 1/(R-2) - 1/(M+2) = 1/60
Multiplying both sides by 60(R-2)(M+2)
=> 60M + 120 -60R + 120 = RM -2M + 2R -4
=> 62M - 62R = RM - 244
=> 62R - 62M = 244 - RM - eq2
Multiplying eq 1 by 31 & eq 2 by 30 & equating both
31RM = 30(244 - RM)
=> 31RM = 30*244 - 30RM
=> 61RM = 30*244
=> RM = 120
Putting in eq 1
60R - 60M = 120
=> R - M = 2
=> R - (120/R) = 2
=> R² - 120 = 2R
=> R² - 2R - 120 = 0
=> R² - 12R + 10R - 120 = 0
=> R(R-12) + 10(R-12) = 0
=> (R+10)(R-12) = 0
R = 12
Rita speed in first round = 12 km/Hr
R - M = 2
=> M = 10
Madhulika speed in first round = 10 km/Hr