Question #89c39

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Answer 1 · 2017-09-26T02:29:59

$20$ and $5$ .

Let the speed of the boat be $x$ $"miles/hour"$ and the speed of the current be $y$ $"miles/hour"$ .

In down stream the trip $(x+y)$ $"miles"$ takes in $1$ hour. so, $825$ $"miles"$ takes $825/(x + y)$ $"hours"$ .

Hence, as per question

$825/(x + y) = 33" "" "(i)$

Again, in the trip back, $(x - y)$ $"miles"$ take $1$ hour. Hence $825$ $"miles"$ take $825/(x - y)$ $"hours"$ .

Hence, as per question

$825/(x - y) = 55" "" "(ii)$

From equation $(i)$ , we get

$825/(x + y) = 33$

or

$x + y = 825/33 = 25" "" "(iii)$

From equation $(ii$ ), we get

$825/(x - y) = 55$

or

$x - y = 825/55 = 15" "" "(iv)$

Now, solving equations $(iii)$ and $(iv)$ , we get

$x = 20 and y = 5$

Hence, the speed of the boat is $"20 miles/hours"$ and the speed of the current is $"5 miles/hours"$ .