A man completed a journey in 10 hours. He travelled first half of the total distance at the rate of 21 km/hr and second half at the rate of 24 km/hr. What is the total distance he travelled in kilometer?

1. A

   220 km

2. B

   224 km

3. C

   230 km

4. D

   234 km

Appeared in: OSSSC Nursing Officer-2021

Explanation

• The problem involves calculating the total distance ('D') of a journey split into two equal halves (D/2).
• The time taken for each half is calculated using the formula: Time = Distance / Speed.
• Time for the first half is (D/2) / 21 = D/42 hours.
• Time for the second half is (D/2) / 24 = D/48 hours.
• The sum of the times for both halves equals the total journey time of 10 hours: D/42 + D/48 = 10.
• Solving this equation for D yields the total distance of 224 km.

Why Other Options Were Wrong

• Option A: This value is incorrect and likely results from a calculation error, such as an arithmetic mistake when solving the equation for the total distance.
• Option C: This is an incorrect result, probably due to an error in the algebraic manipulation or using an incorrect formula, such as wrongly averaging the speeds.
• Option D: This incorrect value could arise from a conceptual error, such as incorrectly calculating the average speed as a simple arithmetic mean ((21+24)/2 = 22.5 km/hr) and then making a subsequent calculation error, as 22.5 × 10 = 225 km, not 234 km.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the ability to calculate total distance traveled based on time and variable speeds over different segments of a journey as background academic context rather than a clinical decision trigger.
• This question assesses fundamental mathematical skills, which are crucial for nurses in clinical practice.
• Accurate calculations are essential for tasks such as determining correct medication dosages, setting IV drip rates, and managing fluid balance, all of which directly impact patient safety.
• What if? If the journey involved traveling for 10 hours at 21 km/hr and another 10 hours at 24 km/hr (equal times, not equal distances), the total distance would be calculated as (10 hr × 21 km/hr) + (10 hr × 24 km/hr) = 210 km + 240 km = 450 km.

How to Approach the Question

• First, identify the given information: total time = 10 hours, speed for the first half (s1) = 21 km/hr, and speed for the second half (s2) = 24 km/hr.
• Recognize that the distance is split into two equal halves. Let the total distance be 'D'.
• Set up an equation using the formula Time = Distance / Speed. The total time is the sum of the time for each half: (D/2)/s1 + (D/2)/s2 = Total Time.
• Substitute the known values into the equation: (D/2)/21 + (D/2)/24 = 10.
• Solve the equation for 'D' to find the total distance.
• As a shortcut, you can calculate the average speed for a journey of two equal distances using the harmonic mean: Average Speed = (2 × s1 × s2) / (s1 + s2). Then, find the total distance by multiplying the average speed by the total time.

Concept Tested & Keywords

• Concept Tested: This question tests the ability to calculate total distance traveled based on time and variable speeds over different segments of a journey.
• Stem keywords: journey, 10 hours, first half, 21 km/hr, second half, 24 km/hr, total distance
• Lead-in keywords: What is

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