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 5 km/hour faster than the bicyclist heading south. At 10:45, they are 47.25 km apart. Find the two bicyclists’ rates.

Question

anonymous · Answer

(Scratching head)

shinalcantara · Answer

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