kakz wrote:1.While on a straight road, Car X and Car Y are traveling at different constant rates. If Car X is now 1 mile ahead of Car Y, how many minutes from now will Car X be 2 miles ahead of Car Y, if Car X is traveling at 50 miles per hour and Car Y is traveling at 40 miles per hour?

As the cars are moving in the same direction, relative speed of the cars = (50 - 40) = 10 miles per hour.

Total distance between them cover = (2 - 1) = 1 mile

Hence, time required = 1/10 hour = 6 minutes

kakz wrote:2. While on a straight road, Car X and Car Y are traveling at different constant rates. If Car X is now 1 mile ahead of Car Y, how many minutes from now will Car X be 2 miles ahead of Car Y, if three minutes ago Car X was 1/2 mile ahead of Car Y?

In three minutes, car X is (1 - 1/2) = 1/2 miles ahead of car Y.
Hence, relative speed of the cars = 1/2 miles per 3 minute = 1 mile per 6 minute

Total distance between them cover = (2 - 1) = 1 mile

Hence, time required = 6 minutes

kakz wrote:Question to Mr. Anurag
Sir if i will change small part of the problem i.e. instead of saying 2 miles I will say, How many minutes from now will Car X be 5 miles ahead of Car Y? Hope you can please show the solution for that for both problems.

I hope you've noticed that in both the cases their relative speeds are determinable and equal. 1 mile per 6 minutes is same as 10 miles per hour.

Hence, whatever is the distance between them is to cover, it'll take same time for both the cases as follows.

Total distance between them to cover = (5 - 1) = 4 mile
Hence, time required = 4/10 hour = 24 minutes