Question

Madhulika and Rita ran a 2 km race twice. Rita completed the first round 2 minutes earlier
than Madhulika. In the second round Madhulika increased her speed by 2km/hr.
Madhulika finished 2 minutes earlier than Rita. Find their speed of running the first round​

Answer 1

Answer:

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

Answer 2

Answer:

Madhulika and Rita ran a 2 km race twice. Rita completed the first round 2 minutes earlier

than Madhulika