How much time did it take a certain car to travel 400 kilometers?

(1) The car traveled the first 200 kilometers in 2.5 hours.
(2) If the car's average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hour less time than it did.

Statement 1: The car traveled the first 200 kilometers in 2.5 hours.
No information about the last 200 kilometers.
INSUFFICIENT.

Statement 2: If the car's average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hour less time than it did.
Since one speed is 20 kilometers greater than the other, the two speeds are likely to be factors of 400 that are 20 apart: 80 and 100.
Time to travel 400 kilometers at a speed of 80 miles per hour = 400/80 = 5.
Time to travel 400 kilometers at a speed of 100 miles per hour = 400/100 = 4 hours.
Time difference = 5-4 = 1 hour. Success!
No other combination of speeds will work.
To illustrate, if the speeds are 5 and 25, the difference in time = 400/5 - 400/25 = 80-16 = 64 hours.
Thus, the only speed that satisfies statement 2 is 80 kilometers per hour.
SUFFICIENT.

The correct answer is B.

siddharth11.sharma@gmail. wrote:How much time did it take a certain car to travel 400 km.
1) The car traveled the first 200 km in 2.5 hrs.
2) If the cars average speed had been 20 km/hr greater then it was, it would have travel led the 400 kilometers in 1 hr less time then it did.

We need to determine how much time it took a car to travel 400 kilometers.

Statement One Alone:

The car traveled the first 200 kilometers in 2.5 hours.

Since we don't know the time it takes to travel the final 200 kilometers, statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

If the car's average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hour less time than it did.

Using the information in statement two, we can set up the following:

r = the average speed of the car

r + 20 = the average speed of the car when traveling 20 kilometers greater than it did

distance traveled = 400 kilometers

Since time = distance/rate, we can express time as the following:

time at normal rate = 400/r

time at faster rate = 400/(r+20)

Since when the car travels at the faster rate, the time is one hour less than when it travels at the normal rate, we can create the following equation:

400/r - 1 = 400/(r+20)

Multiplying the entire equation by r(r+20) gives us:

400(r+20) - r(r+20) = 400r

400r + 8000 - r^2 - 20r = 400r

r^2 + 20r - 8000 = 0

(r + 100)(r - 80) = 0

r = -100 or r = 80

Since we cannot have a negative rate, r = 80 km/hr. So the time it takes the car to travel 400 km is (400 km)/(80 km/hr) = 5 hours. Statement two is sufficient to answer the question.

Answer: B