Max@Math Revolution wrote:If t1 hours are required to travel d miles at v1 miles per hour and t2 hours are required to travel the same d miles at v2 miles per hour, is the overall average speed equal to (v1+v2)/2?
1) t1=t2
2) v1=v2

* A solution will be posted in two days.

Distance formula: distance traveled = time * speed

The answer is D. We can set up two equations for d.

d = t1 * v1

d = t2 * v2

Therefore, we know (by substitution) that t1 * v1 = t2 * v2.

If t1 = t2, as given by (1), then v1 must equal v2. Since the time for each interval is the same, the average speed is simply the average of the two values. So this is sufficient to answer the question.

Likewise, if v1 = v2, as given by (2), then t1 must equal t2. Again, since the time for each interval is the same, the average speed is simply the average of the two values. So this is also sufficient to answer the question.

There are 5 variables (v1, t1, v2, t2, d) and two equations (v1t1=d, v2d2=d) in the original condition. In order to match the number of variables to the number of equations, we need 3 equations. Therefore, there is high chance that E is the correct answer. Using both the condition 1) and the condition 2), we get the condition 1)=the condition 2). The answer is always yes and the conditions are sufficient. Hence, the correct answer is D.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.