Three Cars Leave From A To B In Equal Time Intervals GMAT Problem Solving

Question: Three cars leave from A to B in equal time intervals. They reach B simultaneously and then leave for Point C which is 240 miles away from B. The first car arrives at C an hour after the second car. The third car, having reached C, immediately turns back and heads towards B. The first and the third car meet a point that is 80 miles away from C. What is the difference between the speed of the first and the third car?

1. 60 mph
2. 20 mph
3. 40 mph
4. 80 mph
5. 120 mph

‘Three Cars Leave From A To B In Equal Time Intervals GMAT Problem Solving’ is the topic for GMAT Quantitative Reasoning. GMAT quantitative reasoning section is focused on analyzing the candidates' ability to solve mathematical, and quantitative problems. This topic is a part of the GMAT Problem Solving section. It includes five optional answers and candidates need to choose the appropriate one. Candidates are given 62 minutes to complete this section. GMAT Quantitative Reasoning section of the exam comprises 31 questions.

Solution and Explanation:

Approach Solution 1:

Explanation:

There are three points that have been mentioned in the question. Thus, the first thing that is necessary to be accomplished is calculating the ratio of the first car to that of the second car. Thus, this leaves us with the below-mentioned equation;
(240-80):(240+80).
Upon solving the above-mentioned equation, we get the ratio as: 1:2.
Further, to solve this, let us consider the distance from point A to point B being X.
In addition, consider the interval between the departure of the first car and second car to be represented as t.
Thus, we can highlight the total time taken by the first car as; T.
This implies that the speed of the first car can be calculated as; X/T

Further, this gives us the conclusion that speed of the second car can be calculated as; \(\frac {X}{T-t}\)

Moreover, speed of the third car can be calculated as;\(\frac{X}{T-2t}\)

Thus, we can further calculate the above-mentioned equations as: \(2*\frac{X}{T}=\frac{X}{T-2t}\)

Thus, the first equation that we can get is T=4t……. (1)
In order to get the second equation we can derive with:

\(\frac{240T}{X}-\frac{240(T-t)}{X}=1.....(2)\)

Upon solving the first and second equations:
We get the value X/T=60
Therefore, by substituting the value of X/T, we can easily calculate the speed of the cars.
Speed of first car= 60Km/h
Speed of third car= 2*60= 120 Km/h

Difference = 120-60 = 60Km/h

Correct Answer: A

Approach Solution 2:

Explanation:

Let us consider the representation of the speed of the car in descending order to be z, y and x.
As mentioned in the question the first and the third car meet a point that is 80 miles away from C, which is 240 miles away.
Thus, this yields that x travelled 240-80 and z travelled 240+80.
Ratio of distance = 240-80:240+80=160:320=1:2, so their speed will be in the ratio 2:1.
Thus, considering the speed of car x to be X. thus, the speed of car z will be 2X.
Thus, there is a necessity to solve for Z-X=2X-X=X
If the distance from A to B is D, then equal intervals means:

\(\frac{D}{Z}-\frac{D}{Y}=\frac{D}{Y}-\frac{D}{X}.........\frac{D}{2X}-\frac{D}{Y}=\frac{D}{Y}-\frac{D}{X}........Y=\frac{4X}{3}.....\)

Thus, the ratio of the speed can be highlighted as:\(X:\frac{4X}{3}:2X\)
Thus, to equate and find the value of X, consider the first car arrives at C hour after the arrival of the second car.

\(\frac{240}{X}-240/ \frac{4X}{3}=1\)

\(\frac{240}{X}-\frac{180}{X}=1\)

This, implies that, X=60
Therefore, the answer is 60.

Correct Answer: A

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