Question: A student goes to school at the rate of $ 2\frac{1}{2}km/h $ and reaches 6 min late. If he travels at the speed of $ 3km/h $ he is 10 min early. What is the distance to the school?
Options:
A) $ 4km $
B) $ 3\frac{1}{2}km/h $
C) $ 1km $
D) $ 3\frac{1}{2}km $
Show Answer
Answer:
Correct Answer: A
Solution:
- Let distance of the school be x km.
According to the question,
$ \frac{x}{5/2}-\frac{x}{3}=\frac{16}{60} $
$ \Rightarrow $ $ \frac{2x}{5}-\frac{x}{3}=\frac{4}{15} $
$ \Rightarrow $ $ \frac{6x-5x}{15}=\frac{4}{15} $
$ \therefore $ $ x=4km $