Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 20 miles apart. One and a half hours later, they are again 20 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour?  Choose the correct choice.
A) a) 80-x B) b) 40-x C) c) 26.67-x D) d) 120-x E) e) 40-x/2
Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same.   Here, the two cars approach a distance 20 mi, then move away from each other another distance of 20 miles. That's a total distance of 40 miles in 1.5 hr, which gives a rate of:   R = (40 mi)/(1.5) = 26.67 mph   That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars.   One of the speeds is x, and let's call the other y. We want y.   x + y = 26.67   y = 26.67 - x   Answer =(c) 26.67-x)
<result>C</result>
Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 20 miles apart. One and a half hours later, they are again 20 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour?