Bunuel wrote:

Xavier and Adam are riding motorcycles down the highway at constant speeds. If Xavier is now 2 miles ahead of Adam, how many minutes before Xavier is 3 miles ahead of Adam?

(1) Xavier is traveling at 70 miles per hour and Adam is traveling at 60 miles per hour.

(2) Xavier left 5 minutes before Adam.

Relative Distance = Relative Speed * Time

The relative distance to be covered is 1 mile. We need the time it will take to cover this Relative Distance.

(1) Xavier is traveling at 70 miles per hour and Adam is traveling at 60 miles per hour.

Relative Speed = 70 - 60 = 10 mph

We have the relative distance and relative speed so we can find the time taken.

Sufficient.

(2) Xavier left 5 minutes before Adam.

We know that Xavier left 5 mins before but we don't know for how long Adam has been riding. So we do not know in how much time Xavier covered a relative distance of 2 miles.

Say both have the same speed so their relative speed is 0. In that case, Xavier would have covered the 2 extra miles in 5 mins.

Say Xavier covered 1 mile in 5 mins and hence has a speed of 12 mph. If Adam's speed is 2 mph, Xavier would have covered another 1 mile extra in 6 mins.

In either case, their relative speed is different and hence, time taken for Xavier to cover a relative distance of 1 mile will be different.

Not sufficient.

Answer (A)

can we assume adam speed to be less than or equal to Xavier's?, because the question asks, how much time before was Adam 3 miles behind Xavier, if that were to happen, Adam speed has to be greater than Xavier's to get closer and closer to Xavier to make the question valid. If Adam speed is less than Xavier's , Xavier will be moving away for every minute. Am i correct?