Question : A girl goes from A to B with a speed of 60 km/hr and returns from B to A with a speed of 30 km/hr. If the whole journey takes 5 hours, then what is the distance between A and B?
Option 1: 200 km
Option 2: 100 km
Option 3: 50 km
Option 4: 90 km
Correct Answer: 100 km
Solution :
Total time taken = 5 hours
Speed to go from A to B = 60 km/hr
Speed to go from B to A = 30 km/hr
we know that,
Average speed = $\frac{\text{2 × (Speed to go to A to B) × (Speed to go to B to A)}}{\text{(Speed to go to A to B) + (Speed to go to B to A)}}$
= $\frac{2\times60\times30}{60+30}$
= $\frac{3600}{90}=40$ km/hr
Average speed = 40 km/hr
Now, Distance = Speed × time
= 40 × 5
= 200
The total distance from A to B and B to A is 200 km.
Thus, distance From A to B = $\frac{200}{2}=100$
Hence, the correct answer is 100 km.
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