Question : A and B are 15 km apart and when travelling towards each other, meet after half an hour, whereas they meet two and a half hours later if they travel in the same direction. The faster of the two travels at a speed of:
Option 1: 15 km/h
Option 2: 18 km/h
Option 3: 10 km/h
Option 4: 8 km/h
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Correct Answer: 18 km/h
Solution :
Let the speeds of A and B be $a$ km/h and $b$ km/h respectively.
When moving on opposite sides, relative speed = (a + b) km/h.
When moving on the same sides, relative speed = (a – b) km/h.
According to the question, (Using: Relative speed = $\frac{\text{Relative disatnce}}{\text{Time}}$)
$a + b = \frac{15}{\frac{1}{2}}$
⇒ $a + b = 30$ -------------------------------------------(1)
Also $a – b = \frac{15}{2\frac{1}{2}}$
⇒ $a – b = 6$ ---------------------------------------------(2)
By solving equation 1 and equation 2 we get,
$a$ = 18 km/h and $b$ = 12 km/h
So, the faster of the two travels at a speed of 18 km/h.
Hence, the correct answer is 18 km/h.
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