Question

At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path.The bicyclist heading north is riding 4 km/hour faster than the bicyclist heading south. At 10:30, they are 39 km apart. Find the two bicyclists’ rates.
(A)northbound bicyclist = 15 km/h; southbound bicyclist = 11 km/h
(B)northbound bicyclist = 17 km/h; southbound bicyclist = 11 km/h
(C)northbound bicyclist = 15 km/h; southbound bicyclist = 10 km/h
(D)northbound bicyclist = 16 km/h; southbound bicyclist = 12 km/h

Answer 1

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 = $1\frac{1}{2}$ hours = 3/2 hours,

Since,

$\text{Relative Speed}= \frac{\text{ Relative Distance }}{\text{Relative time}}$

$\implies 2x + 4 = \frac{39}{3/2}$

$\implies 2x+4 = \frac{78}{3}=26$

$\implies 2x = 22\implies x = 11$

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

Answer 2

The question is asking to choose among the following choices that states the two bicyclist's rate and in my further computation and calculation, I would say that the answer would be letter (A)northbound bicyclist = 15 km/h; southbound bicyclist = 11 km/h. I hope this would help you