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Question: Two cars are traveling towards each other. If car A is traveling at a speed of 50 mph and car B is traveling 12% slower, how much time will it take the cars to meet if the initial distance between the two is 705 miles?
- Six hours and 30 minutes.
- Seven hours and 30 minutes.
- Eight hours and 20 minutes.
- Nine hours and 15 minutes.
- Ten hours and 20 minutes.
Solution and Explanation
Approach Solution 1
Car B is moving at a speed of 0.88 *50 = 44 miles per hour.
The following equation can be created if we assume that t is the amount of time, in hours, that it takes for them to travel before they encounter one another:
50t + 44t = 705
94t = 705
t equals 7.5 hours, which is equivalent to 7 hours and 30 minutes.
B is the correct answer.
Approach Solution 2
Let's first find the speed of car B, which is traveling 12% slower than car A.
Speed of car B = 50 mph - 12% of 50 mph
Speed of car B = 50 mph - (0.12 * 50 mph)
Speed of car B = 50 mph - 6 mph
Speed of car B = 44 mph
Now, the combined speed of both cars when traveling towards each other is the sum of their individual speeds:
Combined speed = Speed of car A + Speed of car B
Combined speed = 50 mph + 44 mph
Combined speed = 94 mph
The distance between the two cars is 705 miles, and they are moving towards each other at a combined speed of 94 mph. To find the time it takes for them to meet, we can use the formula:
Time = Distance / Combined speed
Time = 705 miles / 94 mph
Now, let's calculate the time:
Time = 7.5 hours
Since 0.5 hours is equal to 30 minutes, the total time is 7 hours and 30 minutes.
So, the correct answer is B.
Approach Solution 3
First, let's figure out how fast car B is going. It's going 12% slower than car A.
Car B's speed is 50 mph - 12% of 50 mph.
Car B's speed is 50 mph - 0.12 times 50 mph.
Car B's speed is 50 mph - 6 mph.
Car B is going 44 mph.
Now, when both cars are moving towards each other, their total speed is the sum of their individual speeds:
Speed of both cars together = Speed of car A plus Speed of car B
The total speed is 50 mph + 44 mph.
Speed all together: 94 mph
There are 705 miles between the two cars, and they are both going towards each other at a speed of 94 mph. We can use the following method to figure out when they will meet:
Time = Distance / Speed of the whole group
Time = 705 miles x 94 mph
Now, let's figure out how long it took:
7.5 hours = 7.5 hours
Since half an hour is equal to 30 minutes, the total time is 7 hours and 30 minutes.
So, B is the right answer.
“Two cars are traveling towards each other" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.
To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.
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