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