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Question

# Lucknow is at a distance of 300 km from Varanasi. A car start from Varanasi at a speed of 30 km/hour for Lucknow. A second car starts from Lucknow for Varanasi at a speed of 60 km/hour at the same time. Find the time after which both cars meet each other.

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Solution

## Dear student, Here is the solution of your asked query: $\mathrm{Suppose}\mathrm{both}\mathrm{the}\mathrm{car}\mathrm{meet}\mathrm{each}\mathrm{other}\mathrm{after}\mathrm{time}"\mathrm{t}"\mathrm{hour}.\phantom{\rule{0ex}{0ex}}\mathrm{Distance}\mathrm{between}\mathrm{Luckhnow}\mathrm{and}\mathrm{Varanasi}=300\mathrm{km}\phantom{\rule{0ex}{0ex}}\mathrm{Speed}\mathrm{of}\mathrm{car}\mathrm{travelling}\mathrm{from}\mathrm{Varanasi}\mathrm{to}\mathrm{Luckhnow}=30\mathrm{km}/\mathrm{hour}\phantom{\rule{0ex}{0ex}}\mathrm{We}\mathrm{know}\mathrm{that},\mathrm{Distance}\mathrm{travelled}=\mathrm{speed}×\mathrm{time}\phantom{\rule{0ex}{0ex}}\mathrm{So},\mathrm{distance}\mathrm{travelled}\mathrm{by}\mathrm{a}\mathrm{car}\mathrm{from}\mathrm{Varanasi}\mathrm{to}\mathrm{Luckhnow}\mathrm{in}\mathrm{time}"\mathrm{t}"=30\mathrm{t}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Similarly}\mathrm{distance}\mathrm{travelled}\mathrm{by}\mathrm{second}\mathrm{car}\mathrm{from}\mathrm{luckhnow}\mathrm{to}\mathrm{Varanasi}=60\mathrm{t}\phantom{\rule{0ex}{0ex}}\mathrm{So},\mathrm{total}\mathrm{distance}\mathrm{covered}=30\mathrm{t}+60\mathrm{t}=300\mathrm{km}\phantom{\rule{0ex}{0ex}}⇒90\mathrm{t}=300\phantom{\rule{0ex}{0ex}}⇒\mathrm{t}=\frac{300}{90}=\frac{10}{3}\mathrm{hour}=3\frac{1}{3}\mathrm{hour}\phantom{\rule{0ex}{0ex}}\mathrm{Therefore}\mathrm{both}\mathrm{cars}\mathrm{meet}\mathrm{each}\mathrm{other}\mathrm{after}3\frac{1}{3}\mathrm{hours}.$ Regards

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