Amotorboat takes 5 hours to travel 150km 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?

=10km/h

Step-by-step explanation:

Let motor boat speed be represented by x and current y

The speed upstream = Motor boats speed - rate of current

=x-y

The net speed down stream = Motor boats speed + rate of current

=x+y

Let us find the speed upstream =distance/ time taken

=150km/5hrs

=30km/h

Speed down stream= 150km/3h

=50 km/h

The problem forms simultaneous equations.

x-y=30

x+y=50

Using elimination method we solve the equations.

Add the two equations to eliminate y.

2x=80

x=40

Current, y= 50-x

=10km/h

1)

2)

Step-by-step explanation:

 Let' call "b" the speed of the motorboat and "c" the speed of the current.

We know that:

Where "V" is the speed, "d" is distance and "t" is time.

Then:

We know that distance traveled upstream is 150 km and the time is 5 hours. Then, we set up the folllowing equation:

   (Remember that in the trip upstream the speed of the river is opposite to the motorboat)

For the return trip:

 By solving the system of equations, we get:

- Make both equations equal to each other and solve for "c".

- Substitute "c" into the any original equation and solve for "b":

- Substitute "b" into :

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

b). 4320 have a nice day