Speed of boat in still water formula

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. See Answer See Answer See Answer done loading Question:The speed of a boat in still water is v. The boat is to make a round trip in a river whose current travels at speed u. A) Derive a formula for the time needed to make a round trip of total distance D if the boat makes the round trip by moving upstream and back downstream. Express your answer in terms of the variables D, v, and u. B) Derive a formula for The speed of a boat in still water is v. The boat is to make a round trip in a river whose current travels at speed u. A) Derive a formula for the time needed to make a round trip of total distance D if the boat makes the round trip by moving upstream and back downstream. Express your answer in terms of the variables D, v, and u. B) Derive a formula for the time needed to make a round trip of total distance D if the boat makes the round trip by moving directly across the river and back. Express your answer in terms of the variables D, v, and u. Thanks

SOLUTION: 1. The speed of a boat in still water is 10 mph. If it travels on a river 6 miles downstream in the same amount of time it takes to travel 3 miles upstream, what is the speed of th SOLUTION: 1. The speed of a boat in still water is 10 mph. If it travels on a river 6 miles downstream in the same amount of time it takes to travel 3 miles upstream, what is the speed of th • 1. The speed of a boat in still water is 10 mph. If it travels on a river 6 miles downstream in the same amount of time it takes to travel 3 miles upstream, what is the speed of the current? 2. The speed of a boat in still water is 8 mph. If it travels 24 miles upstream and 24 miles downstream in a total of 12 hours, what is the speed of the current? Answer by Theo(12757) ( You can PROBLEM NUMBER 1 ----- let b = speed of the boat in still water. let c = speed of the current ----- rate * time = distance let h = time ----- going downstream, the formula is (b + c) * h = 6 going upstream, the formula is (b - c) * h = 3 ----- since b = 10, these formula become: (10 + c) * h = 6 and (10 - c) * h = 3 ----- since 6 = 2 * 3, then we can substitute (10 - c) * h for 3 to get: (10 + c) * h = (10 - c) * h * 2 ----- this formula becomes: 10h + ch = 20h - 2ch we add 2ch to both sides and we subtract 10h from both sides to get: 3ch = 10h we divide both sides by h to get: 3c = 10 we divide both sides by 3 to get: c = 10/3 ----- our first equation is: (10 + c) * h = 6 we replace c with 10/3 to get: (10 + 10/3) * h...

Downstream/Upstream Boat Speed – Important Formulas Numerical Aptitude Notes for APSC Prelim CSAT Paper, SSC and Competitive Exams Go to Aptitude, Reasoning and Quants Formulas & Notes Still Water: If the speed of the water is zero, i.e. water is stationary, then it is called still water. Stream: The moving water in the river is known as a stream. • Upstream: If a boat or a swimmer moves in the opposite direction of the stream, then it is called upstream, i.e. direction against the stream. • Downstream: If a boar or a swimmer moves in the same direction of the stream, then it is called downstream, i.e. direction along the stream If the speed of a boat in still water is u km/hr and Speed of the stream is v km/hr, • Speed downstream = (u + v) km/hr. • Speed upstream = (u – v) km/hr. If the speed downstream is a km/hr and the speed upstream is b km/hr, then • Boat Speed in still water = ½ (Downstream Speed + Upstream Speed) = 1/2 x (a + b) km/hr. • Rate of stream = ½ (Downstream Speed – Upstream Speed) = 1/2 x (a – b) km/hr. • Average Speed of Boat = ] km/hr, where “v” is the speed of the stream

Boats & Streams is one of the favorite areas of examiners. Questions from this area appear in a significant proportion in the quant section of almost all the competitive exams. Before starting with the questions, go through the basic concepts of the topic. Important Terms • Still Water: If the speed of the water is zero, i.e. water is stationary, then it is called still water. • Stream: The moving water in the river is known as a stream. • Upstream: If a boat or a swimmer moves in the opposite direction of the stream, then it is called upstream. • Downstream: If a boar or a swimmer moves in the same direction of the stream, then it is called downstream. • When the speed of a boat or a swimmer is given, it usually means speed in still water. Formulae Then: • Upstream Speed: It is the speed of the boat against the stream = (u - v) km/hr • Downstream Speed: It is the speed of the boat with the stream = (u + v) km/hr • If upstream is denoted as U S and downstream as D S, then: Speed of boat or swimmer in still water = 1/2 (D s + U s) Speed of stream =1/2 (D s - U s) • If a man is capable of rowing at the speed of u km/hr in still water, rows the equal distance up and down the stream which flows at a rate of v km/hr, then the average speed throughout the journey • A man can row a boat in still water at u km/hr. A stream is flowing at v km/hr and it take t hrs more in upstream than to go downstream for the same distance, then the distance is calculated by = (u 2– v 2)t/2v km • A...

Given: The speed in still water is double the speed of stream Formula: Upstream = (u − v) km/hr Downstream = (u + v) km/hr Where “u” is the speed of the boat in still water and “v” is the speed of the stream Speed of boat in still water = 1/2(Downstream speed + Upstream speed) Speed of stream = 1/2(Downstream speed – Upstream speed) Calculation: Let the downstream speed and upstream speed be 2x and x respectively. 180/(2x + x) + 180/(2x - x) = 24 ⇒ 180/(3x) + 180/(x) = 24 ⇒ 60/x + 180/x = 24 ⇒ 240/x = 24 ⇒ x= 10 Time taken to cover 40 km upstream = 40/10 = 4 hours ∴ The total time it will take to cover 40 km upstream is 4 h.

Table of Contents • • • • • • • • • • • • • • • • • • • • • • • • • How do I find the boat rate in still water? Upstream and Downstream Formula • Upstream (uu2212v) km/hr, where u is the speed of the boat in still water and v is the speed of the stream. • Downstream (u+v)Km/hr, where u is the speed of the boat in still water and v is the speed of the stream. • Speed of Boat in Still Water (Downstream Speed + Upstream Speed) What is the rate in still water? The against current and with current should cancel each other out (again, assuming the current is constant) to get the still water rate. 20+242 442 22 mph. The rate that the boat travels in still water is 22 mph. What is the speed of the boat in still water and the speed of the current? Answer: The speed of the boat in still water or b 10 km/h. The speed of the current or the river 4 km/h. Therefore the speed of the boat when going upstream b r 10 4 6 km/hr. Therefore the distance covered in one hour 6/1 6 km. How do you calculate current in a river? Answer • The distance going upstream and downstream is the same. • Time going upstream is 3 hours. • Time going downstream is 2 hours. • Speed of the boat (r) is 5 miles per hour. • Distance (d) rate (r) X time (t) What is the formula for finding current rate? The against current and with current should cancel each other out (again, assuming the current is constant) to get the still water rate. 20+242 442 22 mph. The rate that the boat travels in still water is 22 mph. What ...