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  3. Mathematics
  4. A man misses a bus by 40 minutes, if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?

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Q. A man misses a bus by 40 minutes, if he travels at $30 kmph$. If he travels at $40 kmph$, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?

Time and Distance

Solution:

Let the distance to be travelled to catch the bus be $x km$.
$\frac{x}{30}-\frac{x}{40}=\frac{30}{60} $
$\frac{4 x-3 x}{120}=\frac{30}{60} \Rightarrow x=60 km$
By travelling $30 kmph$ time taken $=\frac{60}{30}=2$ hours
By taking 2 hours, he is late by $40 min$. So, he has to cover $60 km$ in 1 hour $20 min$ to catch the bus.
The minimum speed $=\frac{60}{\frac{4}{3}}=45 kmph$.