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 6 km/hour faster than the bicyclist heading south. at 10: 15, they are 42.5 km apart. find the two bicyclists' rates

a. northbound bicyclist= 20 km/h; southbound bicyclist= 14 km/h
b. northbound=20 km/h; southbound= 11km/h
c. northbound= 23 km/h; southbound= 17km/h
d. northbound= 20km/h; southbound= 13 km/h

(A) Northbound bicyclist=20 km/hr, southbound bicyclist=14 km/h.

Step-by-step explanation:

The total time taken is= 1 hour 15 min=1.25 hours. Let the distance traveled by bicyclist heading in the south direction is represented by and the distance traveled by the bicyclist heading in north direction be , then according to question +=42.5km.                                                                                                  (1)

Therefore, using speed= ,

Distance traveled by bicyclist heading in the south direction is = speed × time= 1.25×S, where S is the speed of the bicyclist heading in south........(2)

Since, The bicyclist heading in north direction is 6km/hr faster than the bicyclist heading in south direction, therefore,

Speed of bicyclist heading in north direction will be, N=S+6...........(3)

Let the distance travelled by the bicyclist heading in north direction is represented as .

Therefore, = 1.25N

=1.25(S+6)

=1.25S+ 7.5                                                                                           (4)

Now, subtracting (2) from (4), we have

-=1.25S+7.5-1.25S

-=7.5                                                      (5)

Now, from equation (1), we have +=42.5, solving equation (1) and equation (5), we get =25km.

Now, substituting this value of in equation (1),

+=42.5

=42.5-25.0

=17.5km

Now,speed of the bicyclist heading in north direction will be:

=

=

Also, Speed of bicyclist heading in south direction=

=

54 kilometers per hour

step-by-step explanation:

according to rules:

1 km = 1000 meter

which means that 1 meter = 1/1000 km

1 hour = 3600 second [ as 1 hour = 60 min = 60 *60 seconds ]

which means that 1 second = 1/3600 hour

therefore, 1 kilometer/hour =

thus to convert 15 meter per second to kilometer per hour, we multiply 15 to 3.6 kilometer/hour.

15 meter/second=   which is the required answer.

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;