It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more if 200 km is train by done and the rest by car, The of the speed of the train that of the car is

1. A

   2:3

2. B

   3:2

3. C

   3:4

4. D

   4:3

Appeared in: HSSC Staff Nurse - 2015

Explanation

• The problem provides two scenarios that can be translated into two linear equations with two variables (x for train speed, y for car speed).
• The first scenario gives the equation 120/x + 480/y = 8, which simplifies to 15/x + 60/y = 1.
• The second scenario gives the equation 200/x + 400/y = 25/3 (since 8 hours 20 minutes = 8 1/3 hours), which simplifies to 24/x + 48/y = 1.
• By equating the two simplified expressions, we get 15/x + 60/y = 24/x + 48/y.
• Solving this equation for the ratio x/y gives 9/12, which simplifies to 3/4.

Why Other Options Were Wrong

• Option A: The ratio 2:3 is incorrect. This value does not satisfy the system of equations derived from the problem statement.
• Option B: The ratio 3:2 is incorrect. This might be the result of an algebraic error during the simplification or rearrangement of the equations.
• Option D: The ratio 4:3 represents the ratio of the car's speed to the train's speed (y/x).

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Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving simultaneous linear equations derived from word problems involving speed, distance, and time as background academic context rather than a clinical decision trigger.
• While not a clinical question, quantitative aptitude is a key part of nursing entrance exams, testing logical reasoning and problem-solving skills essential for the nursing profession.
• Accurate calculation is a fundamental nursing skill, crucial for medication dosage, IV fluid rate calculations, and interpreting patient data charts.
• What if the question asked for the ratio of the car's speed to the train's speed? The answer would be the inverse, 4:3, highlighting the importance of carefully reading what the question is asking for.

How to Approach the Question

• First, identify the core formula for this problem: Time = Distance / Speed.
• Assign variables to the unknown quantities: let the train's speed be 'x' and the car's speed be 'y'.
• Translate the two scenarios described in the problem into two distinct algebraic equations using your variables.
• Remember to convert all time units to be consistent (e.g., convert 8 hours and 20 minutes into hours only: 8 + 20/60 = 25/3 hours).
• Simplify the two equations. Then, solve this system of two equations to find the relationship between x and y.
• Carefully calculate the final ratio as requested by the question (train speed to car speed, which is x:y).

Concept Tested & Keywords

• Concept Tested: Solving simultaneous linear equations derived from word problems involving speed, distance, and time.
• Stem keywords: journey, km, hours, train, car, speed
• Lead-in keywords: ratio of the speed
• Negative lead-in flag: false

Question ID

QYPVXGbotlllI2atCEsRQ_

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