Rate problem

[romitvsingh]

While on a straight road, car X & car Y are travelling 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?

1) Car X is travelling at 50 miles per hour and car Y is travelling at 40 miles per hour.

2) Three minutes ago car X was 1/2 miles ahead of car Y

Pls explain in detail

[chieftang]

Each statement is sufficient.

1. Every 6 minutes the cars are 1 mile further apart. 12 minutes = 2 miles apart.

2. If 3 minutes = 0.5 miles, then X minutes = 2 miles. X = 12.

[Anurag@Gurome]

While on a straight road, car X & car Y are travelling 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?

1) Car X is travelling at 50 miles per hour and car Y is travelling at 40 miles per hour.

2) Three minutes ago car X was 1/2 miles ahead of car Y

Pls explain in detail

(1) 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; SUFFICIENT.

(2) 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; SUFFICIENT.

The correct answer is D.

[chufus]

A.

Car X travels 50/60 = 5/6 miles per minute
Car Y travels 40/60 = 4/6 miles per minute

Distance travelled by X = x
Distance travelled by Y = x-1

Time taken by both is the same.

Time is distance/speed

so x/(5/6) = x-1/(4/6)

Solve to find x = 5 miles

Distance is 5 miles, speed is 5/6 miles per minute

So > 5(5/6) = 6 minutes

SUFFICIENT

B. 3 minutes ago they were 1/2 miles apart and now they are 1 mile apart. So X gains half a mile every 3 minutes since they are at constant speed.

Hence to add a mile would take 3*2 = 6 Minutes

SUFFICIENT

Pick "D"[/b]