Question 1151632

A boat’s speed in still in water is 4km/h.The boat cruises from A to B along a river flowing at an average speed of X km/h in the direction A to B . If the distance AB is 5 km and the boat takes 2hr more on its return journey,determine x. Hence,find the total time taken for the whole journey.
<pre>From A to B, the boat is travelling WITH the current, so its time to get from A to B is {{{5/(4 + x)}}}
On the return trip (B to A), the boat is travelling AGAINST the current, so its time to get from B to A is {{{5/(4 - x)}}}
We then get the following TIME equation: {{{matrix(1,3, 5/(4 - X) - 5/(4 + X), "=", 2)}}}
{{{matrix(1,3, 5(4 + X) - 5(4 - X), "=", 2(4 - X)(4 + X))}}}
{{{matrix(1,3, 20 + 5X - 20 + 5X, "=", 2(16 - X^2))}}}
{{{matrix(1,3, 10X, "=", 32 - 2X^2)}}}
{{{matrix(1,3, 2X^2 + 10x - 32, "=", 0)}}}
{{{matrix(1,3, X^2 + 5x - 16, "=", 0)}}}
Using the quadratic equation or completing the square, {{{highlight_green(matrix(1,8, X, or, speed, of, current, "=", 2.21699, "km/h"))}}}
{{{highlight_green(matrix(2,10, Time, taken, to, travel, from, A, to, B, "=", 5/(4 + 2.21699), Time, taken, to, travel, from, B, to, A, "=", 5/(4 - 2.21699)))}}}
Now, calculate those 2 times and you should get the total time of the round-trip.