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

Answers

Simple. The two cyclists have covered a distance of 39 miles in 1.5 hours. 39 divided by 1.5 = 26, so 26kph combined speed. Then just divide 26 by 2 = 13kph, which is the average speed of each cyclist. Then add 2kph to the one cyclist and subtract 2kph from the other. One is going at 15kph, the other is going at 11kph. 
let x be the speed of bicyclist A (heading north)
     
y be the speed of bicyclist B (heading south)
 
since A is 5km/hr faster than B
 
x = y + 5 equation 1

time = 9 to 10:45 = 1.75hours since the distance is 47.25km then,
 
x(1.75) + y(1.75) = 47.25 ---equation 2

substitute equation 1 to 2 (y+5)(1.75) + 1.75y
 
= 47.25 1.75y +8.75 + 1.75y
 
= 47.25 3.5y
 
= 47.25 - 8.75 3.5y

= 38.5

y = 11km/hr
 
substitute to equation 1
 
x = y + 5 x

= 11 + 5 x

= 16km/hr
Let x be the rate of the slower bicyclist and
      x + 4 be the rate of the faster bicyclist

Since the bicyclists are headed towards opposite directions, the sum of the distances they covered traveling for one hour and 15 minutes should be equal to 40 km based on the given conditions above. This may be expressed as,
 
                                   (x)(1.25) + (x + 4)(1.25) = 40

Calculating gives x = 14 

Thus, the rate of the bicyclists are 14 km/h and 18 km/h.

Rates of two bicyclists are 18 km per hour and 14 km per hour.

Step-by-step explanation:

At 9:00 on Saturday morning, two bicyclists passes each other in opposite directions on a bicycle path.

Let the speed of a bicyclist heading north is = x km per hour

It is given that the speed of the bicyclist heading south is 4 km per hours less than the speed of the bicyclist heading north.

Therefore speed of bicyclist heading south will be = (x - 4) km per hour

After 1 hour and 15 minutes or 1.25 hours these bicyclists are 40 km apart.

Since distance = speed × time

So the equation will be

x(1.25) + (x - 4)(1.25) = 40

(1.25)(x - 4 + x) = 40

(1.25)(2x - 4) = 40

2x - 4 = \frac{40}{1.25}=32

2x = 32 + 4

2x = 36

x = 18 km per hour will be the speed of the bicyclist heading north.

Speed of the bicyclist heading south = (x - 4) km per hour

                                                             = 18 - 4

                                                             = 14 km per hour

Therefore, rates of two bicyclists are 18 km per hour and 14 km per hour.

ok ok byw

Step-by-step explanation:

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northbound bicyclist is going 15 km/h and the southbound bicyclist is going 11 km/h

(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

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 


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