Ronit and Sonali are 50 km apart. If they walk towards each other, they meet in 5 hours. If Ronit walks at \(\frac{3}{4}\) of his speed and Sonali at \(\frac{1}{4}\) of her speed, they meet in 8 hours 20 minutes. Find the speed of Ronit.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 7 km/hr
Walking towards each other, they close the 50 km at the sum of their speeds. Each meeting time gives one equation in the two speeds \(r\) (Ronit) and \(s\) (Sonali).
First case: \(\displaystyle r+s=\frac{50}{5}=10\)
Second case: 8 hours 20 minutes \(\displaystyle =\frac{25}{3}\) hours, so \(\displaystyle \frac{3r}{4}+\frac{s}{4}=50\times\frac{3}{25}=6\), that is \(3r+s=24\)
Subtracting the first equation: \(2r=14\)
\(r=7\) km/hr