BoatintheRiver Problems Robert has a boat that has a speed of 11 mph in still water If the boat with the motor turned off is placed in a river in which the water flows at 3 mph the boat will drift downstream at 3 mph if the boat is headed downstream with the motor turned on its speed rat ID: 621187
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Slide1
Lesson 92:
Boat-in-the-River ProblemsSlide2
Robert has a boat that has a speed of 11 mph in still water. If the boat, with the motor turned off, is placed in a river in which the water flows at 3 mph, the boat will drift downstream at 3 mph. if the boat is headed downstream with the motor turned on, its speed (rate) downstream would be 14 mph, which is 3 mph plus 11 mph. if the boat is turned around and is headed upstream, it must go against the current; and its speed upstream would be only 8 mph, which is 11mph minus 3 mph. Slide3
Thus, in general, the downstream rate is the speed of the boat plus the speed of the water, and the upstream rate is the speed of the boat minus the speed of the water.
Downstream rate = B + W
Upstream rate = B – W Slide4
The distance downstream equals the rate downstream times the time downstream, and the distance upstream equals the rate upstream times the time upstream. These two statements lead to the following two equations, which can be used to solve almost all boat-in-the-river problems. Slide5
Downstream Equation:
(B + W)T = D
Upstream Equation:
(B – W)T = D
D D
U USlide6
These two equations contain six unknowns. Thus, boat-in-the-river problems must contain six statements of equality, because six equations are required. Slide7
Example:
Robert and Clay could go 60 miles downstream in the same time it took them to go 20 miles upstream. If the speed of their boat was 8 mph in still water, what was the speed of the current and what were their times?Slide8
Answer:
T = 5 hours
W = 4mphSlide9
Example:
The steamboat
Juby
Fountain
could go 70 miles downstream in 5 hours but required 6 hours to go 48 miles upstream. What was the speed of the boat in still water and what was the speed of the current?Slide10
Answer:
B = 11mph
W = 3mphSlide11
Example:
The water in the Flint River flows at 5 kilometers per hour. A speedboat can go 15 kilometers upstream in the same time it takes to go 25 kilometers downstream. How fast can the boat go in still water?Slide12
Answer:
20kphSlide13
HW: Lesson 92 #1-30