The speed of a boat in Stillwater is 25 km/h and the speed of the current is 7 km/h. If a boat goes from place A to B and returns from B to A and it takes six hours 40 minutes in t... The speed of a boat in Stillwater is 25 km/h and the speed of the current is 7 km/h. If a boat goes from place A to B and returns from B to A and it takes six hours 40 minutes in total, find the time taken by the boat to cover twice the distance of AB downstream.
Understand the Problem
The question is asking us to calculate the time taken by the boat to cover twice the distance of AB downstream, given the speed of the boat in still water and the speed of the current. We will first determine the effective speed of the boat when going downstream and then use the total time taken to find the required time for twice the distance.
Answer
The time taken by the boat to cover twice the distance of AB downstream is $$ \frac{2d}{b + c} $$
Answer for screen readers
The time taken by the boat to cover twice the distance of AB downstream is $$ \frac{2d}{b + c} $$
Steps to Solve
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Identify speed values Let the speed of the boat in still water be denoted as $b$ (in km/h) and the speed of the current as $c$ (in km/h).
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Calculate effective speed downstream When the boat is moving downstream, the effective speed is the sum of its speed in still water and the speed of the current. Thus the effective speed is given by: $$ \text{Effective speed downstream} = b + c $$
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Determine distance covered Let the distance from A to B be represented as $d$ (in km). The time taken to travel this distance downstream is: $$ \text{Time taken for distance AB} = \frac{d}{b + c} $$
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Calculate time for twice the distance To find the time taken to cover twice the distance (2d), we use the same effective speed: $$ \text{Time taken for distance 2AB} = \frac{2d}{b + c} $$
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Final expression of time The expression for the time to cover twice the distance downstream becomes: $$ \text{Time for 2AB} = \frac{2d}{b + c} $$
The time taken by the boat to cover twice the distance of AB downstream is $$ \frac{2d}{b + c} $$
More Information
This formula shows how the distance and effective speed of the boat determine the time taken to travel downstream. If the values of the speed of the boat ($b$) and the current ($c$) are substituted alongside the distance ($d$), we can compute the exact time.
Tips
- Not accounting for the current's speed when calculating effective speed may lead to incorrect time estimation. Always ensure to add the speed of the current to the boat's speed in still water.
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