michelleperezmp58
contestada

A motorboat 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?

Respuesta :

smmwaite

Answer:

=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

luisejr77

Answer:

1) [tex]40\ \frac{km}{h}[/tex]

2) [tex]10\ \frac{km}{h}[/tex]

Step-by-step explanation:

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

We know that:

[tex]V=\frac{d}{t}[/tex]

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

Then:

[tex]d=V*t[/tex]

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

 [tex]5(b-c)=150[/tex]  (Remember that in the trip upstream the speed of the river is opposite to the motorboat)

For the return trip:

 [tex]3(b+c)=150[/tex]  

 By solving the system of equations, we get:

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

[tex]5(b-c)=3(b+c)\\\\5b-5c=3b+3c\\\\5b-3b=3c+5c\\\\2b=8c\\\\c=\frac{b}{4}[/tex]

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

[tex]5(b-\frac{b}{4})=150\\\\\frac{3}{4}b=30\\\\b=40\ \frac{km}{h}[/tex]

- Substitute "b" into [tex]c=\frac{b}{4}[/tex]:

[tex]c=\frac{40}{4}\\\\c=10\ \frac{km}{h}[/tex]