Person A and Person B are both at Point A (above). Starting at the same time, Person A drives to point B while Person B drives to point C. Who arrives at his destination first? (1) Person A's average speed is 2 3 that of Person B's. (2) Person B's average speed is 20 kilometers per hour greater than Person A's. Options: A . &nbsp If the question can be answered with statement 1 alone B . &nbsp If the question can be answered with statement 2 alone C . &nbsp If both statement 1 and statement 2 are needed to answer the question and D . &nbsp If the question cannot be answered even with the help of both statements

Person A and Person B are both at Point A (above). Starting at the same time, Pe

Question

Person A and Person B are both at Point A (above). Starting at the same time, Person A drives to point B while Person B drives to point C. Who arrives at his destination first?
(1) Person A's average speed is

\frac{2}{3}

that of Person B's.
(2) Person B's average speed is 20 kilometers per hour greater than Person A's.

Options:

A . If the question can be answered with statement 1 alone

B . If the question can be answered with statement 2 alone

C . If both statement 1 and statement 2 are needed to answer the question and

D . If the question cannot be answered even with the help of both statements

Answer: Option A
:
A
Since AB = BC, triangle ABC is a 45-45-90 triangle. Such triangles have fixed side ratios as follows:
AB: BC: AC

\to

1:1:

\sqrt{2}

Thus, we can call Person A's distance (AB) x, while Person B's distance (AC) is.
Person B has a greater distance to travel
Let's first analyze Statement (1) alone: Person A's average speed is that of Person B's.
This indicates that Person B is traveling 1.5 times faster than Person A. If Person A's rate is r, than Person B's rate is 1.5r. However, recall that Person B also has a greater distance to travel.
To determine who will arrive first, we use the distance formula: Rate x Time = Distance. Whoever has a shorter TIME will arrive first.

\begin{matrix} Person A's time & Person A's time = \frac{D i s t a n c e}{r a t e} = \frac{x}{r} & \frac{D i s t a n c e}{r a t e} = \frac{1.4 x}{1.5 r} = 93 (\frac{x}{r}) \end{matrix}

Since person B is traveling for less time, he will arrive first Statement(1) alone is sufficient.
Let's now analyze Statement (2) alone: Person B's average speed is 20 kilometers per hour greater than Person A's.
This gives us no information about the ratio of Person B's average speed to Person A's average speed. Thus, although we know that Person B's distance is approximately 1.4 times Person A's distance, we do not know the ratio of their speeds, so we cannot determine who will arrive first.
For example, if Person B travels at 25 kmph, Person A travels at 5 kmph. In this case Person B arrives first. However, if Person B travels at 100 kmph, Person A travels at 80 kmph. In this case Person A arrives first.
Therefore, Statement (2) alone is not sufficient.
Since statement (1) alone is sufficient, but statement (2) alone is not sufficient, the correct answer is A.

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