Alice is faster than Bob, Alice and Bob each walk 30 km. The sum of their speeds is 8 km/hr and sum of time taken by them is 16 hours. Then Alice’s speed is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5
Each person’s time is distance divided by speed. The sum of the speeds and the sum of the times give two equations, and together they fix the product of the speeds.
Taking the speeds as \(a\) (Alice) and \(b\) (Bob), in km/h:
\(a+b=8\) (1)
\(\displaystyle \frac{30}{a}+\frac{30}{b}=16\), that is, \(\displaystyle \frac{30(a+b)}{ab}=16\) (2)
Putting (1) into (2): \(\displaystyle \frac{240}{ab}=16\), so \(ab=15\)
Two numbers with sum 8 and product 15 are 5 and 3
Alice is the faster walker, so her speed is 5 km/h.