Question

A row team paddles 30 miles upstream in 2 hours and 30 miles downstream in 45 minutes. How fast can the row team paddle in still water? What is the rate of the current?

Answer 1

Answer:

Rate in still water = 27.5 mph

Current's rate = 12.5 mph

Step-by-step explanation:

Let

x mph = row team rate in still water

y mph = current's rate

Upstream:

Distance = 30 miles

Time = 2 hours

Rate = x - y mph

Then

$30=2(x-y)$

Downstream:

Distance = 30 miles

Time = 45 minutes $=\dfrac{3}{4}$ hour

Rate = x + y mph

Then

$30=\dfrac{3}{4}(x+y)$

From the first equation:

$30=2(x-y)\Rightarrow 15=x-y$

From the second equation:

$30=\dfrac{3}{4}(x+y)\Rightarrow 40=x+y$

Add these two equations:

$15+40=x-y+x+y\\ \\2x=55\\ \\x=27.5\ mph$

Subtract these two equations:

$40-15=x+y-(x-y)\\ \\25=x+y-x+y\\ \\2y=25\\ \\y=12.5\ mph$