a motorboat takes 5 hours to travel 150 Miles going Upstream. the return trip takes 3 hours going Downstream .what is the rate of the boat in still water and what is the rate of the current ?
Answers
Answer:
Speed of boat in still water = 40 mph
Rate of current = 10 mph
Step-by-step explanation:
Let the speed of boat in still water be x & let the speed of the stream be y.
Total Distance = 150 miles
Time taken to travel during upstream = 5 hrs
Speed of the boat during upstream = [tex]\frac{150}{5} = 30\:mph[/tex]
Speed of boat during upstream can be represented as [tex]x - y = 30[/tex] because the boat is moving in the opposite direction of flow of stream.
Time taken to travel during downstream = 3 hrs
Speed of boat during downstream = [tex]\frac{150}{3} = 50\:mph[/tex]
Speed of boat during downstream can be represented as [tex]x+y=50[/tex] because the boat is moving in the same direction of flow of stream.
We got a pair of linear eqns. Let [tex]x-y=30[/tex] be eqn.1 and [tex]x+y=50[/tex] be eqn.2 . Using substitution method ,
From eqn.1 , [tex]x-y=30[/tex]
[tex]=> x = y + 30[/tex]
Putting 'x' in eqn.2 , [tex]x + y = 50[/tex]
[tex]=> y + 30 + y = 50[/tex]
[tex]=> y + y = 50-30[/tex]
[tex]=> 2y = 20[/tex]
[tex]=> y = \frac{20}{2} = 10\: mph[/tex]
Putting y in eqn.1 ,
[tex]x - 10 = 30[/tex]
[tex]=> x = 30 + 10 = 40 \:mph[/tex]
Hence , the speed of boat in still water is 40 mph and speed of stream is 10 mph
Related Questions
The area of a circle is 9π
if and only if, its radius is 3.
true or false
Answers
when 2(3/5 x + 2/3 y - 1/4 x -1 1/2 y + 3 )is simplified, what is the resulting expression?
Answers
Answer:
Simplifying the expression: [tex]2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-1\frac{1}{2}y +3)[/tex] we get [tex]\mathbf{42x-100y-360}[/tex]
Step-by-step explanation:
We need to simplify the expression: [tex]2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-1\frac{1}{2}y +3)[/tex]
First we will solve terms inside the bracket
[tex]2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-1\frac{1}{2}y +3)[/tex]
Converting mixed fraction [tex]1\frac{1}{2} y[/tex] into improper fraction, we get: [tex]\frac{3}{2}y[/tex]
Replacing the term:
[tex]2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-\frac{3}{2}y +3)[/tex]
Now, taking LCM of: 5,3,4,2 we get 60
Now multiply 60 with each term inside the bracket
[tex]2(\frac{3}{5}x\times60+\frac{2}{3}y\times60-\frac{1}{4}x\times60-\frac{3}{2}y\times60 +3\times60)\\2(3x\times12+2y\times20-1x\times15-3x\times30-3\times60)\\2(36x+40y-15x-90y-180)[/tex]
Now, combine like terms
[tex]2(36x-15x-90y+40y-180)\\2(21x-50y-180)[/tex]
Now, multiply all terms with 2
[tex]42x-100y-360[/tex]
So, Simplifying the expression: [tex]2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-1\frac{1}{2}y +3)[/tex] we get [tex]\mathbf{42x-100y-360}[/tex]
NOBODY HAS HELPED ME TODAY ??? please help me !!!
Answers
28/20 = 2x+3/15
28(15)/20 = 2x+3 = 2x+3 = 21
2x=18
x=9
Whos your favorite operator in rainbow six seige
Answers
Answer:
It has to be Maverick how about u
Step-by-step explanation:
Answer:
Niclas "Pengu" Mouritzen
Step-by-step explanation:
P
Find the surface area of a closed box with base width 3 cm, base length 5 cm and height 4 cm.
5 cm
1
4 cm
3 cm
4 cm
5 cm
3 cm
O 74 cm
O 15 cm
O 79 cm
O 94 cm
Answers
Answer:
Surface area of box = 94cm²
Step-by-step explanation:
Given that:
Width of box = 3 cm
Length of box = 5 cm
Height of box = 4 cm
Surface Area = 2lw + 2lh + 2hw
Surface area = 2( lw + lh + hw )
Surface area = 2(5*3 + 5*4 + 4*3) = 2(15+20+12)
Surface area = 2(47) = 94 cm²
Hence,
Surface area of box = 94cm²
What is (2 × 0.1) + (3 × 0.01) + (6 × 0.001) in word form?
Answers
Answer:
two hundred thirty-six thousandths
Step-by-step explanation:
Suppose there are 21 students in your class. If the teacher draws 2 names at random, what is the probability that you and your best friend will be chosen?
1/20
1/105
1/210
2/21
Answers
Answer:
2/21
Step-by-step explanation:
Probability = expected outcome/ possible outcome
????????i don’t understand
Answers
Answer:
to blurry
..............
Write an algebraic expression for s decreased by nine
Answers
Answer:s-9
Step-by-step explanation: Decreased means subtract . and you are subtracting s from 9.
Hope it helps
Which property is demonstrated by the equation (5 + a) + 3 = (a + 5) + 3?
Answers
Answer:
Communitive Property
Step-by-step explanation:
Commutative property = 2 + 3 = 3 + 2 or 2(3) = 3(2)
Associative Property = (2 x 3) 5 = 2 (3 x 5) or (2 + 3) + 5 = 2 + (3 + 5)
Inverse Property = 2 + (-2) = 0 or (2/1)(½) = 1
Basic Definitions:
Commutative Property - Gives you the ability to switch the order of the numbers in an expression.
Associative Property - Let's you move the parenthesis in an expression but not the numbers.
Inverse - Uses numbers like 0 and 1.
Using these basic definitions and examples, we can summarize that the best answer would be Communitive Property
If 24 marbles have a mass of 60g what would be the mass of 60 marbles
Answers
Answer:
300 g
Step-by-step explanation:
First divide the mass of those 12 marbles (60 g) by the number of marbles which have 60 g mass (12 marbles). You'll get the answer as 5 g , which means 5 g is the mass of 1 marble. Now multiply the answer by 60 (specification of marbles). You'll have the answer as 300 g.
i.e.
60 / 12 = 5
5 x 60 = 300
Please help me would be very appreciated.
Answers
Answer:
C
Step-by-step explanation:
i don't need the work just the answer!!
Answers
PLEASE HELP ITS DUE BY MIDNIGHT I HAVE LIKE 30 MINS!!! The linear regression for this print-out relates the amount of oxygen in your spaceship measured in liters as a function of time In hours
Interpret the meaning of the slope in the context of the problem
Answers
Answer:
Please check explanations
Step-by-step explanation:
Here, we want to interpret the meaning of the slope
The slope generally refers to the change in y values with corresponding change in x value
with respect to this question, we can see that the slope is negative
What this mean is that the rate of change in the level of oxygen measured in liters is decreasing with an increase in the time
This means that as more time elapses, more oxygen is used up leading to a decrease in the liters of oxygen present
What expression represents the value of y?
Answers
The expression that represents the solution of y is y = √wz
How to determine the value of y?The triangle represents the given parameter
Also, we can see that the figure combines two right-angled triangles is
By the theorem of the right-angled triangle
w : y = y : z
Express the above ratio as a fraction
So, we have the following equation
w / y = y / z
Cross multiply in the above equation
So, we have
y² = wz
Take the square roots
y = √wz
Hence, the solution of y is y = √wz
Read more about right-angled triangle at
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Mmmm! I love apple cider punch this time of year, and so do all my neighbors. My recipe calls for two quarts of apple cyder, three teaspoon of cinnamon, and one pint of lemon-lime soda. This will make enough for 8 people to share. In my neighborhood, however, there are 36 people. How much do I need for each ingredient to make enough for everyone?
Answers
Answer:
j
Step-by-step explanation:
Simplify (6⁴)³
A. b
B. b³
C. b⁹
D. b¹²
Answers
it would be b^12
Hope this helps <3
please help
if right i give brainliest i need help
Answers
Answer:
A-J=4
B-G=50
C-F=2
D-I=32
E-H=8
An airplane prepares for landing. When it begins its descent towards the airport, the plane's
altitude is 27,000 feet. After descending at a steady rate for 6 minutes, its altitude is 19,000
feet. Write an equation for the altitude of the plane. What will the altitude of the plane be after
descending for 12 minutes?
Answers
it descended 8,000 feet in 6 minutes
so in 12 minutes it would of descended 16,000 feet, it’s doubled
19,000-8000= 11,000
The required equation represents the descent motion of the airplane is y = 27000 - 1333.333x and 11000 feet.
Given that,
An airplane prepares for landing. When it begins its descent towards the airport, the plane's altitude is 27,000 feet. After descending at a steady rate for 6 minutes, its altitude is 19,000 feet. Write an equation for the altitude of the plane.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The slope of the motion of the airplane,
m = 27000 - 19000 / 6 = 1333.33
The equation of the plane is given as,
y - y₁ = m (x - x₁)
Substitute the value in the above equation,
y - 27000 = -1333.33[x - 0]
y = 27000 - 1333.33x
Now put x = 12 in above equation,
y = 27000 - 1333.33[12]
y = 11000
Thus, the required equation represents the descent motion of the airplane as y = 27000 - 1333.333x and 11000 feet.
Learn more about slopes here:
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The figure shows a truss used in the construction of a building. The measure of ∠1 is 39°. Find the measure of ∠2.
Answers
Answer:
39
Step-by-step explanation:
Since the first measure is 39 that means the second is 39 because its the same.
Find c.
Round to the nearest tenth:
2 cm
15°
105
Answers
Answer:
0.5cm
Step-by-step explanation:
Using the sine rule
Answer:
c = 0.5 cm
Step-by-step explanation:
Using the Sine rule in the triangle, then
[tex]\frac{c}{sin15}[/tex] = [tex]\frac{2}{sin105}[/tex] ( cross- multiply )
c × sin105° = 2 × sin15° ( divide both sides by sin105°
c = [tex]\frac{2sin15}{sin105}[/tex] ≈ 0.5 cm ( to the nearest tenth )
Can you please help me I am struggling so much. what does n equal in this equation?
-6 > n/15
Answers
Answer:
n < − 90
Step-by-step explanation:
hope this helps and have a great day!
Help foR 100 pointttttttt
Answers
Answer:
nothing is here you'd have to put something to see if people can help
Answer:
ye
Step-by-step explanation:
On the blueprints for a building, 8 inches represents 28 feet. If the blueprints show a distance of 16 inches
between the two walls, how many feet separate the walls?
Answers
Answer:
56 feet
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
what does y equal?......
Answers
Answer:
37
Step-by-step explanation:
Question 1
1 pts
A furniture company has 15 trucks that can make
120 deliveries each day. How many trucks would
they need to make 160 deliveries each day?
Answers
Hi , I have geometric question
What is x angel ?
Answers
solve for y and x explain your thinking
Answers
Answer: X=2.5, Y= 6.5
Step-by-step explanation:
It seems the triangle on the left is being transformed and a scale factor of 0.5 or 1/2 is being used since the 6 is half of 12. Therefore you divide 5 by 2 to get 2 and the 13 by 2 to get 6.5.
If 2+√2 and 2-√2 are the roots of the quadratic equation
-3x²+11x +c=0, find the value of c. The ans is -6,may you show me the steps?
Answers
hope it will help you..........
The half-life of a radioactive kind of iodine is 60 days. How much will be left after 240 days, if you start with 480 grams of it?
Answers
Answer:
30 grams
Step-by-step explanation:
half life is 60 days so every 60 days the amount 480 grams will be half
in 240 days will decay 240 /60 = 4 times
once 480 /2 = 240
twice 240 /2 = 120
trice 120 / 2 = 60
four times 60/2 = 30 grams will be left
