# A boat travels upstream, against the current, at a speed of 4 miles per hour. On the return trip, the boat travels downstream, with the current, at 10 miles per hour. The speed of the current remains constant. What is the speed of the current?

Mar 9, 2017

The speed of the boat is 7 mph

#### Explanation:

Let the speed of the boat be $b$
Let the speed of the current be $c$

Condition 1 is where water is trying to make the boat go backwards but the boat is winning

Condition 2 is where the water is making the boat go forwards. The boat's motor is making it go forward even faster.

condition 1$\text{ } b - c = 4$
condition 2$\text{ "ul(b+c=10) larr" add}$
$\text{ } 2 b + 0 = 14$

divide both sides by 2

$\frac{2 b}{2} = \frac{14}{2}$

$b = 7$
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Relative to the water the boat travels at the same speed. Relative to the land it travels at different speeds.