Two cyclists 84 miles apart start riding toward each other at the same. one cycles 2 times as fast as the other. if they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?

The faster cyclist's speed is 14mph

Step-by-step explanation:

Before I explain this, remember that Distance=Time*Speed.

For now let's suppose the slower cyclist's speed is x mph, and the faster cyclist's speed is 2x mph, because he/she is going 2 times faster.

Both cyclists have been biking for 4 hours, so to find the distance they both travelled in that time, we multiply each of their speeds by 4 (hrs).

So for the slower cyclist, it is x*4=4x miles

And for the faster cyclist, it is 2x*4=8x miles

They cyclists meet after the 4 hours, which means that if you add the distances they travelled in that 4 hours together, you will get 84 miles.

Let's make an equation out of this: 4x+8x=84

Now we solve for x:

4x+8x=84

12x=84

x=7

Now we know that x=7, so all we have to do is go back to the beginning, and remember when I said, we would suppose the slower cyclist's speed is x mph and the faster cyclist's speed is 2x mph? Exactly. We plug 7 in for x and we get 7 mph for the slower cyclist's speed and 14 mph (7*2) for the faster cyclist's speed.

Hope this made sense :)