Linda and Dave leave simultaneously from the same starting point biking in opposite directions. Linda bikes at 6 miles per hour and Dave bikes at 8 miles per hour. how long will it take them to be 27 miles apart from each other?
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Think of the two on a number line. Both start at 0 and then move in opposite directions.
The distance that LInda travels (we'll assume she's going to the right) is 6t. (t=time and rate*time=distance).
Similarly, the distance that Dave travels (we'll assume he's going to the left) is 8t.
Remember that both distances are measured from the zero point. To find their distance from each other, we'll add up the two distances from 0.
Therefore, their distance from each other is 6t+8t, or 14t.
Now we want to know when the distance is 27. Since we have just found that d=14t (d=distance), we can solve for t.
27=14t, so 27/14=t.
And to check, after 27/14 hours, LInda is 81/7 miles away and Dave is 108/7 miles away. Adding the two distances yields 189/7, or 27 miles.