Question

If rajiv rows at his usual rate, he can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. If rajiv could make his usual rowing rate twice of what it is for his 24-mile round trip, the 12 miles downstream would then take only one hour less than the 12 miles upstream. What is the speed of the current in miles per hour?

Answer 1

Answer:

At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his 24-mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles

Answer 2

The speed of the current in miles per hour is 2.667 miles per hour

Solution:

Let the speed of Rahul in still water be  "x" mph

Let the speed of the current be  "y" mph

Then,

Speed upstream  =  x - y

Speed downstream  = x + y

Distance = 12 miles

Time taken to travel upstream - Time taken to travel downstream = 6 hours

$\frac{12}{x - y }- \frac{12}{x + y} = 6\\\\Simplify\\\\24 = 6(x^2 - y^2 ) \\\\x^2 = y^2 + 4y ------ eqn\ 1$

If rajiv could make his usual rowing rate twice of what it is for his 24-mile round trip, the 12 miles downstream would then take only one hour less than the 12 miles upstream

Therefore,

Now he doubles his speed,

New speed = 2x

Speed upstream = 2x - y

Speed downstream = 2x + y

Time taken to travel upstream - Time taken to travel downstream = 1 hour

$\frac{12}{2x-y} - \frac{12}{2x+y} = 1 \\\\Simplify\\\\4x^2 = y^2+24y ------- eqn\ 2$

Multiply eqn 1 by 4

$4x^2 = 4y^2 + 4y\\\\4x^2 = 4(y^2 + y) ------ eqn\ 3$

From Equation 2 and 3,

$y^2 + 24y = 4(y^2 + y) \\\\3y^2 = 8y\\\\3y = 8\\\\y = \frac{8}{3} = 2.667$

Thus speed of the current in miles per hour is 2.667 miles per hour

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