Problem Solving

Ronald and Sonam run a race that is 2000m long. Ronald gives Sonam a start of 200m and beats her by 30 seconds. Next, Ronald gives Sonam a start of 3 minutes and is beaten by 1000m. What are the respective times in minutes in which Ronald and Sonam can separately complete the race?

A. 4, 5
B. 5, 9
C. 6, 9
D. 8, 10
E. 9, 12

Let the speeds of Ronald and Sonam in m/s be a and b respectively.

We have 2 equations:
1) \(\frac{2000}{a}\) = \(\frac{1800}{b}\) - 30
2) \(\frac{1000}{a}\) = \(\frac{2000}{b}\) - 180

Solving these, we get a = \(\frac{25}{3}\) and b = \(\frac{20}{3}\)

Hence, time taken will be
Ronald: \(\frac{2000}{a}\) = 4mins
Sonam: \(\frac{2000}{b}\) = 5mins

That is option A

Let the speed of Sonam be N m/second. When Ronald runs 2000 m, Sonam runs (1800 - 30N). When Ronald runs 1000 m, Sonam runs (2000 - 180N).

Therefore:

2000/1000 = (1800 -30N)/(2000 - 180N)

Solving for N, we get: N = 6.66 m/second.

Thus, Sonam's speed = 400 m/minute and she would take 5 minutes to cover the distance.

Answer: A