Question: During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine's average speed for the entire trip?
- (180-x)/2
- (x+60)/4
- (300-x)/5
- 600/(115-x)
- 12,000/(x+200)
“During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 2021”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
It is asked In terms of x, what was Francine's average speed for the entire trip?
Let x be 50, so now 50% of the distance is traveled at 40mph
and 50% traveled at 60mph.
The average speed for the entire trip will be a tiny bit LESS than the average of the two speeds when the same distance is travelled at two different speeds.
So, Since (40+60)/2 = 50
Over the course of Francine's journey, the average speed must have been little around 50 mph.
Now all we need to do is incorporate the value of x in each option to see which results in an average speed that is just below 50.
Out of all options E is correct.
12,000/(x+200) = 12,000/(50+200) = 48.
The correct is 12,000/(x+200).
Correct Answer: E
Approach Solution 2:
There is another approach to answering this question which is Pretty simple and uses arithmetic approach
Let's say the distance is 100 miles overall.
The result is that Francine covered x miles at 40 mph and 100 x miles at 60 mph.
Average speed is calculated as Total Distance x Total Time.
Traveled distance overall is 100
Total time taken = Time taken to travel (x miles at 40 mph + (100-x)miles at 60 mph)
= x/40 + (100-x)/60
= (60x + 4000 - 40x)/2400
= 4000+20x / 2400
= 200+x / 120
Avg. speed = 100 / (200+x / 120)
= 12000/200+x
The correct is 12,000/(x+200).
Correct Answer: E
Approach Solution 3:
Let x=50, so that 50% of the distance is traveled at 40mph and 50% is traveled at 60mph.
When the same distance is traveled at two different speeds, the average speed for the entire trip will be just a bit LESS than the average of the two speeds.
Since (40+60)/2 = 50, the average speed for Francine's entire trip must be just a bit less than 50.
Now plug x=50 into the answers to see which yields an average speed just a bit less than 50.
Only E works:
12,000/(x+200) = 12,000/(50+200) = 48.
The correct is 12,000/(x+200).
Correct Answer: E
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