Two men P and Q start together from place A at 3 km/h and 3.75 km/h respectively for place B. Q reaches half an hour before P. What is the distance that each one has covered?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 7.5 km
Both men cover the same distance from A to B, and time = distance ÷ speed. Q is faster, so the difference of the two times is the half hour by which Q arrives earlier. Let the distance be \(d\) km:
Time taken by P \(=\displaystyle\frac{d}{3}\) h; time taken by Q \(=\displaystyle\frac{d}{3.75}=\frac{4d}{15}\) h
P takes half an hour longer than Q: \(\displaystyle\frac{d}{3}-\frac{4d}{15}=\frac{1}{2}\)
\(\displaystyle\frac{5d-4d}{15}=\frac{d}{15}=\frac{1}{2}\)
So the distance each covers is \(d=7.5\) km