Question : Amita travels from her house at $3 \frac{1}{2}$ km/hr and reaches her school 6 minutes late. The next day she travels at $4 \frac{1}{2}$ km/hr and reaches her school 10 minutes early. What is the distance between her house and the school?
Option 1: 5.6 km
Option 2: 4.8 km
Option 3: 5.4 km
Option 4: 4.2 km
Correct Answer: 4.2 km
Solution :
Given:
Speed 1 $=3 \frac{1}{2}$ km/hr $= 3.5$ km/hr reaches 6 min late
Speed 2 $=4 \frac{1}{2}$ km/hr $= 4.5$ km/hr reaches 10 min early
Distance $=\frac{\text{(Speed 1 × Speed 2)}}{\text{(Difference of speeds)}}$ × time difference
$\therefore$ Distance $=\frac{\text{(3.5 × 4.5)}}{(4.5-3.5)} × \frac{16}{60}=4.2$
Hence, the correct answer is 4.2 km.
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