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.
Here's another approach:
Target question:
How long did it take to travel 400km
To find the travel time, we need to know the average speed traveled.
Let x = the average speed traveled.
Rephrased target question:
What is the value of x?
Statement 1: The car travelled the first 200km in 2.5hrs
No info about the 2nd half of the trip, so we can't determine the overall average speed.
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: If the car's average speed had been 20 km/h faster, it would have travelled the 400km in 1 hour less time.
Let's start with a word equation:
(travel time at
x km/h) - 1 = (travel time at
x+20 km/h)
Since time = distance/speed, we can now write:
(400/x) - 1 = 400/(x+20)
IMPORTANT: At this point, we need only determine whether or not this equation will yield 1 or 2
valid values of x. If it yields only 1
valid value, then statement 2 is sufficient. If it yields 2
valid values, then statement 2 is not sufficient.
Rewrite as: (400-x)/x = 400/(x+20)
Cross multiply: (400)(x) = (400-x)(x+20)
Simplify: 400x = 8000 + 380x - x^2
Rewrite: x^2 + 20x - 8000 = 0
Factor: (x + 100)(x - 80) = 0
So, x = -100 or 80
Since x cannot be negative,
it must be the case that x = 80
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
