Can someone show me how to solve this? A boat took 5 hours to travel 60km up a river, against the current. The return trip took 3 hours. Find the speed of the boat in still water and the speed of the current.
Answers
And even though you haven't asked to be shown how to do it,
I'll go ahead and do that too:
Call the speed of the boat (through the water) 'B'.
Call the speed of the current (the water) 'C'.
When the boat is going 'up' the river, against the current,
his speed past the riverbank is (B - C).
When the boat is going 'down' the river, the same way as the current,
his speed past the riverbank is (B + C).
The problem says it took him 5 hours to travel 60 km against the current.
Distance = (speed) x (time)
60 km = (B - C) x (5 hours)
The problem also says it took him 3 hours to return.
The distance to return is the same 60 km.
The other direction is the same direction as the current,
so his speed on the return is (B + C).
Distance = (speed) x (time)
60 = (B + C) x (3)
Now we have two equations, so we can find 'B' and 'C'.
5B - 5C = 60
3B + 3C = 60
Multiply each side of the first equation by 3, and
multiply each side of the second equation by 5:
15B - 15C = 180
15B + 15C = 300
Add the second equation to the first one:
30B = 480
B = 480/30 = 16 km per hour.
Subtract the second equation from the first one:
-30C = -120
C = -120/-30 = 4 km per hour.
The speed of the boat through the water (B) is 16 km per hour.
The speed of the water past the riverbank is 4 km per hour.
Check:
-- When the boat is going along with the current, his speed past the riverbank
is (16 + 4) = 20 km per hour. In 3 hours, he covers (3 x 20) = 60.
-- When the boat is going against the current, his speed past the riverbank
is (16 - 4) = 12 km per hour. In 5 hours, he covers (5 x 12) = 60 km.
yay !
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y = 4x + 6
What is the solution to the system of equations?
(−3, 18)
(−3, −18)
(3, −18)
(3, 18)
Answers
For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The solution of the system of equation y = 5x + 3 and y = 4x + 6 is (3,18).
What is a System of equations?
Inconsistent System
For a system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.
The solution of the system of equations can be done as shown below, therefore,
Equation 1: y = 5x + 3
Equation 2: y = 4x + 6
Substitute the value of y from the first equation in the second equation, therefore,
y = 4x + 6
5x + 3 = 4x + 6
5x - 4x = 6 - 3
x = 3
Substitute the value of x in any one of the equation,
y = 5(3) + 3
y = 15 + 3
y = 18
Hence, the solution of the system of equation y = 5x + 3 and y = 4x + 6 is (3,18).
Learn more about System of equation:
#SPJ2
y=5x+3
y= 4x+6
Let's solve y=5x+3 for y
Substitute 5x+3 for y in y=4x+6
y=4x+6
5x+3=4x+6
Add -4x
5x+3-4x=4x+6-4x
x+3=6
Add -3
x+3-3=6-3
x=3
Now substitute 3 for x in y=5x+3
y=5x+3
y= (5)(3)+3
y= 15+3
y= 18
Answer D
(3,18)
I hope that's help:)