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A motorboat travels 280 kilometers in 5 hours going upstream and 936 kilometers in 9 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

User Arjunkhera
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1 Answer

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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.


upstream\text{ }speed=x-y

downstream speed = speed of the boat in still water + speed of the current.


downstream\text{ }speed=x+y

Let's calculate the upstream and the downstream speed of the motorboat based on the given distance and time traveled.


upstreamspeed=(280km)/(5hrs)=(56km)/(h)
downstreamspeed=(936km)/(9hrs)=(104km)/(h)

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:


\begin{gathered} 56=x-y \\ 104=x+y \end{gathered}

To solve for x and y, we can use the elimination method.

1. Eliminate the variable "y" by adding the two equations.


(x-y)+(x+y)=56+104
2x=160

2. Divide both sides by 2.


(2x)/(2)=(160)/(2)
x=80

The value of x is 80.

3. Let's solve for "y" by replacing "x" with 80 in any of the two equations above.


104=x+y
104=80+y
\begin{gathered} 104-80=y \\ 24=y \end{gathered}

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.

User Mayhewsw
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