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?

Question

Genesis Allen · Accepted Answer

The speed of the boat is 7 mph

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#" "b-c=4# condition 2#" "ul(b+c=10) larr" add"# #" "2b+0=14# divide both sides by 2 #(2b)/2=14/2# #b=7# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Relative to the water the boat travels at the same speed. Relative to the land it travels at different speeds.

Jace Anderson · Answer

undefined Let $ s $ be the speed of the boat in still water and $ c $ be the speed of the current.

When the boat travels upstream, the effective speed is $ s - c = 4 $ mph.
When the boat travels downstream, the effective speed is $ s + c = 10 $ mph.

From these equations, we can form a system of equations:

$$ s - c = 4 $$
$$ s + c = 10 $$

Adding these equations eliminates $ c $:

$$ (s - c) + (s + c) = 4 + 10 $$
$$ 2s = 14 $$
$$ s = 7 $$

Substituting $ s = 7 $ into one of the equations to solve for $ c $:

$$ 7 + c = 10 $$
$$ c = 10 - 7 $$
$$ c = 3 $$

Therefore, the speed of the current is $ \boxed{3} $ miles per hour.