Question

the speed of a stream is 3 mph. a boat travels 11 miles upstream in the same time it takes to travel 17 miles downstream. what is the speed of the boat in still water

Answer 1

Answer:

14mph

Explanation:

let speed in still water be represented as y

The speed of the stream is given as 3mph

distance traveled by boat upstream = 11 Miles

distance traveled by boat downstream = 17 miles

∴ speed when the boat travels upstream = y-3

speed when the boat travels downstream = y+3

speed = $\frac{distance}{time}$

time = $\frac{distance}{speed}$

time taken to go upstream = $\frac{11}{y - 3}$

time taken to go downstream = $\frac{17}{y + 3}$

assuming that time taken to travel upstream = time taken to travel downstream

$\frac{11}{y - 3}$ = $\frac{17}{y + 3}$

by cross multiplication,

11(y+3)=17(y-3)

11y + 33 = 17y - 51

17y - 11y = 33 + 51

6y=84

y= 84/6

y=14

there the speed in still water is 14mph