At 9:00 on Saturday morning, two bicyclists heading in opposite direction pass each other on a bicycle path. The bicyclist heading north is riding 4km/hour faster than the bicyclist heading south. At 10:15, they are 40 km apart. Find the two bicyclists' rates.
A: Northbound bicyclist = 18 km/h; southbound bicyclist = 14 km/h
B: northbound bicyclist = 19 km/h; southbound bicyclist = 15 km/h
C: northbound bicyclist = 18 km/h; southbound bicyclist = 13 km/h
D: northbound bicyclist = 16 km/h; southbound bicyclist = 10 km/h
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I found this online it might help:
v = the rate of the bicyclist heading south
v + 4 = the rate of the bicyclist heading north (4 km/hour faster)
d = 40 km the sum of the distances that each of the bicyclists passes
t = 10:15 - 9:00 = 1 hr 15 min = 1.25 hr
since the rate = distance/time follows distance = rate*time and we have
v*t + (v + 4)*t = d
v*1.25 + (v + 4)*1.25 = 40
by solving we find
v = 14 km/hour
click here to see the step by step solution of the equation
v + 4 = 14 + 4 = 18 km/hour.
The rate of the bicyclist heading south is 14 km/hour.
The rate of the bicyclist heading north is 18 km/hour.
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