A boat takes 10 hours to travel 100 km downstream. It takes 15 hours to travel 75 km upstream. Then the speed of the boat in still water is :

Appeared in: RRB Staff Nurse Kolkata-2015

Explanation

The speed of the boat in still water is the average of its downstream and upstream speeds.
First, calculate the downstream speed: Distance / Time = 100 km / 10 hours = 10 km/h.
Next, calculate the upstream speed: Distance / Time = 75 km / 15 hours = 5 km/h.
Finally, calculate the speed in still water: (Downstream Speed + Upstream Speed) / 2 = (10 + 5) / 2 = 7.5 km/h.
5 km/h is the same as 7 1/2 km/h.

Option A: This is the boat's downstream speed (100 km / 10 h = 10 km/h), not its speed in still water. This value includes the push from the current.
Option B: This is the boat's upstream speed (75 km / 15 h = 5 km/h), not its speed in still water. This value represents the boat's speed while fighting against the current.
Option C: This value (2.5 km/h or 2 1/2 km/h) represents the speed of the stream, not the speed of the boat in still water. It is calculated as (Downstream Speed - Upstream Speed) / 2.

Visual 1: Diagram: A simple vector diagram showing: 1) Downstream: Boat Speed Vector + Stream Speed Vector = Total Downstream Speed. 2) Upstream: Boat Speed Vector - Stream Speed Vector = Total Upstream Speed. This helps visualize how the current affects the boat's speed.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Speed, Distance, and Time: Relative Speed in Still and Moving Water as background academic context rather than a clinical decision trigger.
This question assesses general aptitude and problem-solving skills, which are essential for nurses in various non-clinical aspects of their roles, such as resource management and data interpretation.
While not directly clinical, the logical reasoning required is similar to that used in calculating drug dosages or infusion rates, where understanding rates and variables is critical.
What if the question asked for the speed of the stream? The calculation would be (Downstream Speed - Upstream Speed) / 2, which is (10 - 5) / 2 = 2.5 km/h.

How to Approach the Question

First, identify the key information given: downstream distance and time, and upstream distance and time.
Recall the basic formula: Speed = Distance / Time.
Use this formula to calculate the downstream speed first.
Then, use the formula again to calculate the upstream speed.
Remember the specific formula for finding the speed of the boat in still water: (Downstream Speed + Upstream Speed) / 2.
Substitute the calculated speeds into this formula to find the final answer and match it with the given options.

Concept Tested & Keywords

Concept Tested: Speed, Distance, and Time: Relative Speed in Still and Moving Water
Stem keywords: boat, downstream, upstream, speed of the boat in still water, 100 km, 10 hours, 75 km, 15 hours
Lead-in keywords: the speed of the boat in still water is

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Attempt every question from this paper in a timed mock, then review the full solution for each one.