Travel ratios

[Striver]

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.

[Anurag@Gurome]

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.

Distance, D = 400 kms
Let time taken = Y and the speed = S

(1) The car traveled the first 200 kilometers in 2.5 hours.
This statement only gives the time for first 200 kms but there is no info about the remaining 200 kms; NOT sufficient.

(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.

S = 400/T
(S + 20) = 400/(T - 1)
400/T + 20 = 400/(T - 1)
(400 + 20T)(T - 1) = 400T
400T + 20T² - 400 - 20T = 400T
T² - T - 20 = 0
(T - 5)(T + 4) = 0
T = 5, -4(not possible); SUFFICIENT.

The correct answer is B.

[bubbliiiiiiii]

Hello Sir,

I approached the solution as you have.

But, how did you conclude that the quadratic equation (in terms of T) has one positive and one negative root. It consumed significant amount of time for me to figure that out by actually solving the quadratic equation. I solved the equation to ensure that it does not have two positive roots in which case the answer would be E!

[Anurag@Gurome]

Hello Sir,

I approached the solution as you have.

But, how did you conclude that the quadratic equation (in terms of T) has one positive and one negative root. It consumed significant amount of time for me to figure that out by actually solving the quadratic equation. I solved the equation to ensure that it does not have two positive roots in which case the answer would be E!

Hello!

I've edited the reply, I hope now it's clear.

Thanks,

[bubbliiiiiiii]

Yes, it is. Thank you.

[GMATGuruNY]

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.