Two Cyclists Start from the Same Place in Opposite Directions; One Goes towards North at 18 km/h and the Other Goes towards South at 20 km/h GMAT Problem Solving

Question: Two cyclists start from the same place in opposite directions; one goes towards north at 18 km/h and the other goes towards south at 20 km/h. What time will they take to be 47.5 km apart?

1. 1 h
2. 1 1/4 h
3. 2 h 23 min
4. 23 1/4 h
5. 24 h

Correct Answer: B

Solution and Explanation:
Approach Solution 1:
The problem statement states that:
Given:

• Two cyclists start from the same place in opposite directions.
• One goes towards the north at 18 km/h and the other goes towards the south at 20 km/h.

Asked:

• the time they take to be 47.5 km apart.

Let's solve this question using the reasoning approach-
Cyclist 1 heads north at 18 km/h, while Cyclist 2 heads south at 20 km/h.
They will be 38 kilometres apart in one hour. They will be 76 kilometres apart in 2 hours.
As a result, the required time should be less than 2 hours.
We are asked how long it will take them to travel 47.5 kilometres.
Only B is less than 2 hours and more than 1 hour according to the answer choices.
As a result, the answer will be B.
Therefore, the time they take to be 47.5 km apart is 1 1/4 h

Approach Solution 2:
There is another fairly simple arithmetic approach to solve this question-
Given:

• Two cyclists start from the same place in opposite directions.
• one goes towards the north at 18 km/h and the other goes towards the south at 20 km/h.

Find Out:

• the time they take to be 47.5 km apart.

Let's evaluate further-
It takes 1 hour to travel 18 + 20 km.
To travel 47.5 kilometres, they must take
\(\frac{1}{38}\)*47.5
= 1\(\frac{1}{4}\)

Approach Solution 3:

The problem statement informs that:
Given:

• Two cyclists start from the same place in opposite directions.
• One goes towards the north at 18 km/h and the other goes towards the south at 20 km/h.

Asked:

• the time they take to be 47.5 km apart.

The cyclists leave at the same time, moving in opposite directions. Hence, the times for each are identical.

Let, time (for each), in hours be t 

Let the distance  covered by the 1^st cyclist be d₁ 

Let the distance  covered by the 2^nd cyclist be d2

NORTH BOUND CYCLIST:
rate • time = distance
=>18t = d₁  ---- (i)

SOUTH BOUND CYCLIST:
rate • time = distance 
=>20t = d₂ ---- (ii)

They will be 47.5 km apart when the sum of their distances is 47.5.
=>d₁ + d₂ = 47.5 ----- (iii)

Substituting (i)  and (ii) ( for d₁ and d₂ ) in equation (iii)
=>18t + 20t = 47.5
=>38t = 47.5
=>t = 47.5/38
=>t = 1\(\frac{1}{4}\) hours

Therefore, the time they take to be 47.5 km apart = 1\(\frac{1}{4}\) hours.

“Two cyclists start from the same place in opposite directions; one goes towards north at 18 km/h and the other goes towards south at 20 km/h”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions facilitate the candidates to analyse information to solve numerical problems. GMAT Quant practice papers help the candidates to get acquainted with different types of questions that improve their mathematical learning.

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