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## Ronald and Sonam run a race that is 2000m long. Ronald gives Sonam a start of 200m and beats her by 30 seconds

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### Ronald and Sonam run a race that is 2000m long. Ronald gives Sonam a start of 200m and beats her by 30 seconds

by Mikrislac » Wed Jul 29, 2020 9:09 am

00:00

A

B

C

D

E

## Global Stats

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

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### Re: Ronald and Sonam run a race that is 2000m long. Ronald gives Sonam a start of 200m and beats her by 30 seconds

by terminator12 » Wed Jul 29, 2020 8:49 pm
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

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### Re: Ronald and Sonam run a race that is 2000m long. Ronald gives Sonam a start of 200m and beats her by 30 seconds

by Mikrislac » Fri Jul 31, 2020 4:30 pm
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.