Question

A boat travels 12 Mph in still water. It can travel 18 miles upstream in the same time that it can travel 24 miles downstream. What is the current of the water?

Answer 1

Answer:

$1 \dfrac{5}{7}\ mph$

Step-by-step explanation:

Let x mph be the current's rate.

Upstream:

Distance = 18 miles

Rate = 12 - x mph

Time $=\dfrac{18}{12-x}$ hours

Downstream:

Distance = 24 miles

Rate = 12 + x mph

Time $=\dfrac{24}{12+x}$ hours

Time is the same, so

$\dfrac{18}{12-x}=\dfrac{24}{12+x}\\ \\18(12+x)=24(12-x)\\ \\216+18x=288-24x\\ \\18x+24x=288-216\\ \\42x=72\\ \\x=\dfrac{12}{7}=1 \dfrac{5}{7}\ mph$