Question

A boat travels 4 km upstream and 4 km back. The time for the round trip is 4 hrs. The speed of the stream is 4 ​km/hr. What is the speed of the boat in still​ water?

Answer 1

since time = distance/speed,
4/(x-4) + 4/(x+4) = 4
x = 5.123

check:
4/1.123 + 4/9.123 = 3.56 + 0.44 = 4.00

Answer 2

speed of boat in still water ---- x km/h
so speed upstream = x-4 km/h
speed downstream = x+4 km/h

4/(x+4) + 4/(x-4) = 4 , lots of 4's there
multiply each term by (x+4)(x-4)
4(x-4) + 4(x+4) = 4(x+4)(x-4)
divide each term by 4 and expand
x-4 + x+4 = x^2 - 16
x^2 -2x -16 = 0

solve for x, use whatever method you like to solve quadratics
obviously rejecting the negative value of x

Answer 3

time = distance / rate

[4 / (s - 4)] + [4 / (s + 4)] = 4

(s + 4) + (s - 4) = (s + 4) (s - 4)

2 s = s^2 - 16

s^2 - 2s - 16 = 0

use the quadratic formula to find s