Question 760966
A stream flows at a rate of 4mph. A boat travels 70 miles downstream and returns in a total time of 6hr. What is the speed of the boat in still water?

Let x be the speed of boat in still water.
Then, the speed of the boat downstream = {{{x+4}}} (since it flows with the current) and speed while returning upstream = {{{x-4}}}

Time taken to travel 70 km downstream = {{{70/(x+4)}}}
Time taken to travel 70 km upstream = {{{70/(x-4)}}}

Total time = {{{70/(x+4) + 70/(x-4) = 6}}}

{{{70*(x-4) + 70*(x+4) = 6*(x+4)*(x-4)}}}

{{{140*x = 6(x^2 - 16)}}}

{{{6*x^2 - 140*x - 96 = 0}}} We can solve this using the standard formula for solving quadratic equations.

*[invoke quadratic "x", 6, -140, -96]



The roots of the equation are x = 24, x = -0.67

Since x cannot be negative, the speed of the boat in still water = {{{24}}} mph