Two cyclists start at the same point and travel in opposite directions. One cyclist travels 3 km/h slower than the other. If the two cyclists are 183 kilometers apart after 3 hours, whats is the rate of each cyclist?
Let
x ------> Rate of the slower cyclist
y ------> Rate of the faster cyclist
Remember that
In this problem the rate is the same that the speed
so
x=y-3 ------> equation 1
Let
d -----> distance from the start after 3 hours slower cyclist
183-d -----> distance from the start after 3 hours faster cyclist
speed slower cyclist
x=d/3
speed faster cyclist
y=(183-d)/3
substitute the values of speed in equation 1
d/3==(183-d)/3-3
solve for d
multiply by 3 on both sides
d=183-d-9
2d=183-9
2d=174
d=87 km
therefore
speed slower cyclist -----> 87/3=29 km/h
speed faster cyclist ----> (183-87)/3=32 km/h