Answer:
(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 [tex]D_{S}[/tex] and the distance traveled by the bicyclist heading in north direction be [tex]D_{N}[/tex], then according to question [tex]D_{N}[/tex]+[tex]D_{S}[/tex]=42.5km. (1)
Therefore, using speed= [tex]\frac{Distance}{time}[/tex],
Distance traveled by bicyclist heading in the south direction is[tex]D_{S}[/tex] = 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 [tex]D_{N}[/tex].
Therefore, [tex]D_{N}[/tex]= 1.25N
=1.25(S+6)
=1.25S+ 7.5 (4)
Now, subtracting (2) from (4), we have
[tex]D_{N}[/tex]-[tex]D_{S}[/tex]=1.25S+7.5-1.25S
[tex]D_{N}[/tex]-[tex]D_{S}[/tex]=7.5 (5)
Now, from equation (1), we have [tex]D_{N}[/tex]+[tex]D_{S}[/tex]=42.5, solving equation (1) and equation (5), we get [tex]D_{N}[/tex]=25km.
Now, substituting this value of [tex]D_{N}[/tex] in equation (1),
[tex]D_{N}[/tex]+[tex]D_{S}[/tex]=42.5
[tex]D_{S}[/tex]=42.5-25.0
[tex]D_{S}[/tex]=17.5km
Now,speed of the bicyclist heading in north direction will be: [tex]\frac{Distance}{Time}[/tex]
=[tex]\frac{25}{1.25}[/tex]
=[tex]20km/hr[/tex]
Also, Speed of bicyclist heading in south direction=[tex]\frac{17.5}{1.25}[/tex]
=[tex]14km/hr[/tex]
