Two cyclists, 64 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?

Let "x" be the slower rate
the faster rate is "3x"

x+3=2x
64/2=32
2x=32/2
x=16 and 3x=48

This question was marked wrong on my homework and I'm not sure why. please help me

1 answer

you are mixing up all kinds of unrelated numbers, and then throwing darts at the calculations.

If x is the slower rate, then 3x is the faster rate. So far so good. Now consider that distance = time * speed, and the total distance covered is 64 miles. Since the time for both riders is 2 hours, we have

2*x + 2*3x = 64
8x = 64
x = 8

So, the speeds are 8 mi/hr and 24 mi/hr. In 2 hours, the riders cover 16+48 = 64 miles.

In some bizarre fashion you came up with the distances at the end, but not the speed of the faster rider, which is what they asked for.