Reiko - DS

[subramanian.k.viswa]

HI, I was stuck with this question in MGMAT CAT. I am not very happy with the explanation provided. Can some please clarify??

Reiko drove from point A to point B at a constant speed, and then returned to A along the same route at a different constant speed. Did Reiko travel from A to B at a speed greater than 40 miles per hour?

(1) Reiko's average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour.

(2) It took Reiko 20 more minutes to drive from A to B than to make the return trip.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

MGMAT Explanation: Correct Answer (A) .. But i selected (E)
(1) SUFFICIENT: Say the trip is d miles long in each direction, so that the round-trip distance is 2d miles. According to this statement, Reiko took (2d miles)/(80 miles/hour) = d/40 hours to drive the entire round trip.

Reiko could not have driven from B to A in zero time, so it must have taken her less than d/40 hours to drive from A to B. Therefore, her speed on the trip from A to B must have been (d miles)/(LESS than d/40 hours) = 1/(LESS than 1/40 hours) = GREATER than 40 miles per hour.

(Note: when dividing by a "less than" number, flip the sign to "greater than." If we had been dividing by a "greater than" number, we would have flipped the sign to "less than.")

MY CONTENTION: This explanation could be valid vice-versa as well right?? For instance:
Reiko could not have driven from A TO B in zero time, so it must have taken her less than d/40 hours to drive from B TO A. Therefore, her speed on the trip from B TO A must have been (d miles)/(LESS than d/40 hours) = 1/(LESS than 1/40 hours) = GREATER than 40 miles per hour.

Which means either of the two trips can be greater than 40 miles per hour, right??

Would appreciate if someone can help clarify this.

[tim]

BOTH of the two trips had to be greater than 40 mph..