Question : Durga walks 5 km from her home to school in 60 minutes, then bicycles back home along the same route at 15 km/hr. Her sister Smriti makes the same round trip but does so at half of Durga's average speed. How much time does Smriti spend on her round trip?
Option 1: 120 minutes
Option 2: 40 minutes
Option 3: 160 minutes
Option 4: 80 minutes
Correct Answer: 160 minutes
Solution :
Durga's walking speed = 5 km/hr and her speed in bicycle = 15 km/hr
Distance between home and school = 5 km
$\therefore$ Her average speed = $\frac{2xy}{x+y}= \frac{2\times5\times15}{5+15} = 7.5$ km/hr
So, Smriti's speed = $\frac{7.5}2=3.75$ km/hr
$\therefore$ Time taken by Smriti on the round trip = $2\times(\frac{5}{3.75})= \frac{8}{3}$ hrs $=(\frac{8}{3})\times60=160$ minutes
Hence, the correct answer is 160 minutes.
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