Answer: (A)northbound bicyclist = 15 km/h; southbound bicyclist = 11 km/h
Step-by-step explanation:
Let the speed of the bicycle that is going to the south = x km/h
Thus, according to the question,
The speed of north going bicycle = ( x + 4 ) km/h
Since, they are going opposite to each other,
Hence, the relative speed of the both bicycle = (x + x + 4) km/h = (2 x+ 4) km/h
Now, after crossing each other at 10:30 AM, they are 39 km apart.
⇒ Relative distance = 39 km,
And, the relative time = 1 hour 30 minutes = [tex]1\frac{1}{2}[/tex] hours = 3/2 hours,
Since,
[tex]\text{Relative Speed}= \frac{\text{ Relative Distance }}{\text{Relative time}}[/tex]
[tex]\implies 2x + 4 = \frac{39}{3/2}[/tex]
[tex]\implies 2x+4 = \frac{78}{3}=26[/tex]
[tex]\implies 2x = 22\implies x = 11[/tex]
Therefore, the speed of south going bicycle = x km/h = 11 km/h
And, the speed of north going bicycle = (x + 4) km/h = 15 km/h
