Question

33. BOATING On a certain river, a motorboat can travel 34 miles per hour with the current and 28 miles per hour against the current. Find the speed of the motorboat in still water and the speed of the current.​

Answer 1

Step-by-step explanation:

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Answer 2

Answers:

Speed of boat in still water = 31 mph

Speed of current = 3 mph

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Step-by-step explanation:

b = speed of the boat in still water

c = speed of the current

When going with the current, the boat is sped up since the current is helping push it where it wants to go. It gets a speed boost.

The equation in this case is b+c = 34 since the boat travels 34 mph with the current.

The other equation is b-c = 28 where the current is now slowing down the boat to 28 mph.

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This is our system of equations

`\begin{cases} b+c = 34\\b-c = 28\end{cases}`

Add the equations straight down.

• The b terms add to 2b.
• The c terms cancel out (since they add to 0).
• The right hand sides add to 62.

We end up with 2b+0c = 62 or 2b = 62.

This solves to b = 31, which is the speed of the boat in still water.

Use this to find c.

b+c = 34

31+c = 34

c = 34-31

c = 3 mph is the speed of the current

Or you could say:

b-c = 28

31-c = 28

-c = 28-31

-c = -3

c = 3 mph