If Bill traveled 15 miles per hour faster and it took him 1/3 less tim GMAT Problem-Solving

Question: If Bill traveled 15 miles per hour faster and it took him 1/3 less time, how fast was he going on the initial trip?

A. 15 mph
B. 20 mph
C. 25 mph
D. 30 mph
E. 45 mph

Answer: D

Solution and Explanation:

Approach Solution 1:
Use the facts in the question to help you answer the current GMAT question. Several areas of mathematics can use these issues. This query relates to time and distance. The way the options are presented makes it difficult to decide which is the best. Applicants need to be able to understand the proper strategy for getting the desired result. Only one of the five potential responses is accurate.
Give Bill's speed be s.
Let the distance voyaged be d.
Initially:
Distance voyaged = d
Speed = s
Subsequently, time = d/s
Second Outing
Distance voyaged = d
Speed = s + 15 (since he voyaged 15 miles/hour quicker than his underlying pace)
Along these lines, time = d/(s+15)
As indicated by the issue,
Time required in the subsequent outing is ⅓ less than initial trip
⟹ d/(s+15) = d/s - (⅓ * d/s)
⟹ 1/(s+15) = 1/s - (1/3* 1/s)
⟹ 1/(s+15) = (3 − 1)/3s
⟹ 1/(s+15) = 2/3s
⟹ 3s = 2 (s+15)
⟹ 3s = 2s+30
⟹ 3s−2s = 30
⟹ s = 30
Hence, the speed in the underlying excursion 30mph
Correct option: D

Approach Solution 2:
Use the facts in the question to help you answer the current GMAT question. Several areas of mathematics can use these issues. This query relates to time and distance. The way the options are presented makes it difficult to decide which is the best. Applicants need to be able to understand the proper strategy for getting the desired result. Only one of the five potential responses is accurate
Distance is equal to speed times time. If the old speed was x miles per hour, the new speed will be x+15 miles per hour.
He would have taken ⅔ of 30 min =20 minutes or ⅔ * ½ = 1/3 hours to travel the distance if he had traveled 30 minutes (12 1 2 hours) in the beginning.
Since distances are equivalent, ½ ∗ x = ⅓ ∗ (x+15)
-> 3x = 2x + 30
-> x= 30
Correct option: D

Approach Solution 3:
Answer the current GMAT question using the information in the question. These problems can be used in a variety of mathematical topics. time and distance is involved in this question. It is challenging to choose the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate course of action to achieve the intended outcome. Out of the five possible answers, only one is true.
Let's assume that Bill's initial speed was "x" miles per hour, and he covered a distance "d" in time "t". Therefore, we can write:
d = xt (equation 1)
Now, if Bill travels 15 miles per hour faster, his new speed would be "x + 15" miles per hour. Also, if he takes 1/3 less time to cover the same distance, his new time would be (2/3)t. Therefore, we can write:
d = (x + 15)(2/3)t (equation 2)
Since both equations 1 and 2 represent the same distance "d", we can equate them and solve for "x":
xt = (x + 15)(2/3)t
xt = (2/3)xt + 10t
(1/3)xt = 10t
x = 30
Therefore, Bill's initial speed was 30 miles per hour. The answer is 30mph.
Correct option: D

“If Bill traveled 15 miles per hour faster and it took him 1/3 less tim" - 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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