Ananyaa travels a certain distance at a speed of 3 kmph and reaches her destination late by 15 minutes. If she travels at a speed of 4 kmph, she reaches her destination 15 minutes earlier. Find the distance that Ananyaa is traveling to reach her destination.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 6 km
The distance is the same at both speeds, so the difference between the two travel times is the 30 minutes between being 15 minutes late and 15 minutes early.
Let the distance be \(d\) km. Time at 3 km/h \(=\frac{d}{3}\) h and time at 4 km/h \(=\frac{d}{4}\) h
15 min late and 15 min early differ by 30 min, so \(\displaystyle \frac{d}{3}-\frac{d}{4}=\frac{1}{2}\)
\(\displaystyle \frac{4d-3d}{12}=\frac{d}{12}=\frac{1}{2}\), so \(d=6\) km