singhmaharaj wrote:On his trip from Alba to Benton, Julio drove the first x miles at an average rate of 50 miles per hour and the remaining distance at an average rate of 60 miles per hour. How long did it take Julio to drive the first x miles?
1) On the trip, Julio drove for a total of 10 hours and drove a total of 530 miles.
2) On his trip, it took Julio 4 more hours to drive the first x miles than to drive the remaining distance.
Statement 2: On his trip, it took Julio 4 more hours to drive the first x miles than to drive the remaining distance.
It's possible that julio took 5 hours to travel the first x miles and 1 hour to travel the remaining distance.
It's possible that Julio took 10 hours to travel the first x miles and 6 hours to travel the remaining distance.
Since the time to travel the first x miles can be different values, INSUFFICIENT.
Statement 1: On the trip, Julio drove for a total of 10 hours and drove a total of 530 miles.
Average speed for the whole trip = d/t = 530/10 = 53 miles per hour.
This is a MIXTURE problem.
Two speeds (50mph and 60mph) are combined to form a mixture with an average speed of 53mph.
To determine how much time must be spent at each speed, we can use ALLIGATION.
Let S = the slower speed and F = the faster speed.
Step 1: Plot the 3 speeds on a number line, with F and S on the ends and the speed for the mixture (53mph) in the middle.
S 50---------53----------60 F
Step 2: Calculate the distances between the values on the number line.
S 50----
3----53----
7-----60 F
Step 3: Determine the ratio of the two given speeds.
The ratio of S to F is the RECIPROCAL of the distances in red.
S:F = 7:3.
Implication:
Of the 10 hours of travel time, 7 hours are traveled at 50mph and 3 hours are traveled at 60mph.
Thus, Julio spent 7 hours traveling the first x miles at 50mph.
SUFFICIENT.
The correct answer is
A.
Please note the following:
Almost NO MATH is needed for statement 2 if we understand how WEIGHTED AVERAGES work.
Given a SLOWER SPEED, a FASTER SPEED, and an AVERAGE SPEED, we can always determine the required TIME RATIO for the slower speed and the faster speed.
In general:
If part of a trip is traveled at x mph, the rest of the trip is traveled at y mph, and the average speed for the whole trip is z mph, the following ratio can be determined:
(time spent traveling at x mph)/(time spent traveling at y mph).
Other alligation problems:
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