Question 19478
Let the speed of the boat be x mph
let the speed of the current be y mph
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Then while going downstream,
distance downstream=16miles
speed=(x+y) [since the current helps the boat]
time taken=d/s=16/(x+y).......[1]
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while going upstream,
distance upstream=4 miles
speed=(x-y) [since the current is in the opposite direction of the boat]
time taken=d/s=4/(x-y).........[2]
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Now we have been told that the total time taken is 48 minutes
48 minutes means : (48/60)hour=(4/5)hour
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Add up both the times we got (equations 1 and 2)
{{{(16/(x+y))+(4/(x-y))=4/5}}}
{{{(16(x-y)+4(x+y))/((x+y)(x-y))=4/5}}}
{{{(16x-16y+4x+4y)/(x^2-y^2)=4/5}}}
{{{(20x-12y)=4/5(x^2-y^2)}}}
Now we have been told in the question that the speed of the current (y) is 15 mph
So we get,
{{{(20x-12(15))=4/5(x^2-(15)^2)}}}
{{{20x-180=4/5(x^2-225)}}}
opening the brackets
{{{20x-180=4/5x^2-4/5(225)}}}
{{{20x-180=4/5x^2-4(45)}}}
{{{20x-180=4/5x^2-180}}}
now '-180' cancels off
{{{20x=4/5x^2}}}
{{{100x=4x^2}}}
{{{25x=x^2}}}
which can be written as
{{{25x=x*x}}}
cancelling out the x we get,
{{{25=x}}}
{{{x=25}}}
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And so we get the top speed of the boat(x) = 25 mph
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Hope this helps,
Prabhat</font>