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: 15, they are 40 km apart. find the two bicyclists’ rates.

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