Two Athletes Cover the Distance from A to B at the Rate of 10 and 15 kmph GMAT Problem Solving

Question: Two athletes cover the distance from A to B at the rate of 10 and 15 kmph respectively. What is the distance from A to B, if one of the athletes takes 15 minutes longer than the other?

  1. 1.5 Km
  2. 3.5 km
  3. 7.5 km
  4. 11 km
  5. 15 Km

Correct Answer: C

Solution and Explanation:
Approach Solution 1:

The problem statement states that:
Given:

  • Two athletes cover the distance from A to B at the rate of 10 and 15 kmph respectively.
  • One of the athletes takes 15 minutes longer than the other.

​Find out:

  • The distance from A to B.

Let’s consider the distance from A to B to be D km.

\(\frac{D}{10}-\frac{D}{15}=\frac{15}{60}\)

This implies,\(\frac{D*(3-2)}{30}=\frac{1}{4}\)  

This implies, D = \(\frac{30}{4}\)

Therefore, D = 7.5 km

Here in the above equation, we can see that the distance between A and D, has been averaged by 10 and 15. The equation becomes, D/10 and D/15 which is equal to 15/60. By doing cross-multiplication we get D equals 30/4. Hence the value of distance (D) is equal to 7.5 kilometers.

Approach Solution 2:
This is a quantitative question, based on the speed, time, and distance section of the math. This particular question is on relative speed.

From the above question, it can be derived that two athletes covered a distance of 10 kilometers in an hour and 15 kilometers in an hour.

If we consider, the distance to be d. Hence, according to the question, when d is equated with 10 and 15, the equation further becomes d/10 – d/15, which equals 15/60.

Hence furthermore, when equated (3d – 2d)/30. Then distance becomes 15/60 * 30. This gives the result of the problem to be 7.5 kilometers.

Approach Solution 3:
The problem statement implies that:
Given:

  • Two athletes cover the distance from A to B at the rate of 10 and 15 kmph respectively.
  • One of the athletes takes 15 minutes longer than the other.

​Find out:

  • The distance from A to B.

Speed of A = 10 kmph
Speed of B = 15 kmph

We can solve the problem by using the formula:
Distance = Speed x Time.

Let the distance be x km.

As per the condition of the question, we can say:
=> x/10 – x/15 = 15/60

=> (3x – 2x)/30 = 15/60

=> x/30 = 15/60

=> x = 15/60 * 30

=> x =  7.5 km

Hence, the distance from A to B = 7.5 km

“Two athletes cover the distance from A to B at the rate of 10 and 15 kmph”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This question has been taken from the book “501 GMAT Questions”. To solve the GMAT Problem Solving questions, the candidates must have a solid knowledge of basic mathematics. The candidates can analyse several sorts of questions from the GMAT Quant practice papers that will enable them to improve their mathematical knowledge.

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