A runner can complete his race in 16 hours. If his speed is decreased by 1/5th, he can cover 40 km less distance in the same time. What was the speed of the runner in the beginning?

1. A

   15 km/h

2. B

   12 km/h

3. C

   18 km/h

4. D

   5 km/h

Appeared in: UP CHO - 10 September 2021

Explanation

• The problem requires setting up an equation based on the relationship: Distance = Speed × Time.
• Let the original speed be 's'. The original distance is 16s. The new speed is s - (1/5)s = (4/5)s, and the new distance is 16 × (4/5)s = (64/5)s.
• The difference in distance is given as 40 km, leading to the equation: 16s - (64/5)s = 40.
• Solving the equation (80s - 64s)/5 = 40 gives 16s = 200, which results in s = 12.5 km/h.

Why Other Options Were Wrong

• Option A: If the original speed was 15 km/h, the original distance would be 15 × 16 = 240 km. The new speed would be 15 - (1/5)*15 = 12 km/h, and the new distance would be 12 × 16 = 192 km. The difference is 240 - 192 = 48 km, which is not 40 km.
• Option B: If the original speed was 12 km/h, the original distance would be 12 × 16 = 192 km. The new speed would be 12 - (1/5)*12 = 9.6 km/h, and the new distance would be 9.6 × 16 = 153.6 km. The difference is 192 - 153.6 = 38.4 km, which is not 40 km.
• Option C: If the original speed was 18 km/h, the original distance would be 18 × 16 = 288 km. The new speed would be 18 - (1/5)*18 = 14.4 km/h, and the new distance would be 14.4 × 16 = 230.4 km. The difference is 288 - 230.4 = 57.6 km, which is not 40 km.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving word problems involving speed, distance, and time as background academic context rather than a clinical decision trigger.
• This type of calculation demonstrates the importance of breaking down a complex problem into smaller, manageable steps.
• It reinforces the skill of translating word problems into mathematical equations, a fundamental skill in many scientific and technical fields, including dosage calculations in nursing.
• What if the speed was decreased by 1/4th instead of 1/5th? The new speed would be (3/4)s. The equation would be 16s - 16*(3/4)s = 40, which simplifies to 16s - 12s = 40, or 4s = 40, making the original speed s = 10 km/h.

How to Approach the Question

• First, identify all the given values and the unknown variable. Here, time = 16 hours, distance difference = 40 km, and the unknown is the original speed (let's call it 's').
• Translate the word problem into mathematical expressions. 'Decreased by 1/5th' means the new speed is s - (1/5)s = (4/5)s.
• Use the fundamental formula: Distance = Speed × Time to set up expressions for the original distance (16s) and the new distance (16 × (4/5)s).
• Formulate an equation based on the relationship given in the problem: Original Distance - New Distance = 40 km.
• Solve the resulting algebraic equation for the unknown variable 's'.
• Finally, check your answer by plugging it back into the problem statement to ensure it satisfies all conditions.

Concept Tested & Keywords

• Concept Tested: Solving word problems involving speed, distance, and time.
• Stem keywords: runner, speed, time, distance, 16 hours, decreased by 1/5th, 40 km less
• Lead-in keywords: What was

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