Respuesta :
Let x = the speed of the boat in still water while y = the rate/speed of the current in km/h.
Recall that:
upstream speed = speed of the boat in still water - speed of the current.
[tex]upstream\text{ }speed=x-y[/tex]downstream speed = speed of the boat in still water + speed of the current.
[tex]downstream\text{ }speed=x+y[/tex]Let's calculate the upstream and the downstream speed of the motorboat based on the given distance and time traveled.
[tex]upstreamspeed=\frac{280km}{5hrs}=\frac{56km}{h}[/tex][tex]downstreamspeed=\frac{936km}{9hrs}=\frac{104km}{h}[/tex]Hence, the upstream speed is 56 km/hour. The downstream speed is 104 km/h.
From the equation above, we can form the following equations:
[tex]\begin{gathered} 56=x-y \\ 104=x+y \end{gathered}[/tex]To solve for x and y, we can use the elimination method.
1. Eliminate the variable "y" by adding the two equations.
[tex](x-y)+(x+y)=56+104[/tex][tex]2x=160[/tex]2. Divide both sides by 2.
[tex]\frac{2x}{2}=\frac{160}{2}[/tex][tex]x=80[/tex]The value of x is 80.
3. Let's solve for "y" by replacing "x" with 80 in any of the two equations above.
[tex]104=x+y[/tex][tex]104=80+y[/tex][tex]\begin{gathered} 104-80=y \\ 24=y \end{gathered}[/tex]The value of y is 24.
Answer:
The rate of the boat in still water is 80 km per hour. The rate of the current is 24 km per hour.
