Question

The speed of a river current is 8 mph. If a boat travels 20 miles downstream in the same time that it takes to travel 10 miles​ upstream, find the speed of the boat in still water.

Answer 1

Answer:

9 mph

Step-by-step explanation:

-Let x be the speed of the boat upstream.

-Since the time upstream and downstream is equal, we will equate their time functions to solve for x:

-Speed upstream=x-8

-Speed downstream=x+8

#We then equate as follows:

$Time =\frac{Distance}{Speed}\\\\Time_1=Time_2\\\\\\\frac{10}{x-8}=\frac{20}{x+8}\\\\10(x+8)=20(x-8)\\\\10x+80=20x-160\\\\10x=240\\\\x=24\ mph$

Hence, the speed of the boat in still water is 9 mph