Trains Boats and Streams Practice Test 3 with solutions

Question : 29 of 40

Marks: +1, -0

Samir can travel 12 miles dowstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. But when he could double his rowing rate for his 24-mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. Find the speed of the current in miles/hour.

$2 2/3$
$2 1/3$
$1 2/3$
$1 1/3$

Validate

Solution:

Let x km/hr and y km/hr be the speed of rowing in still water and speed of the current respectively;
then

{12}/{x-y}-{12}/{x+y}

= 6
⇒

{24y}/{x^2-y^2}

= 6
⇒

x^2

y^2 + 4y

... (i)
Again,

{12}/{2x-y}-{12}/{2x+y}

= 1
⇒

{24y}/{4x^2-y^2}

= 1
⇒

x^2

{y^2+24y}/4

... (ii)
From equations (i) and (ii), we get,

y^2+4y

{y^2+24y}/4

⇒

3y^2

= 8y
∴ y =

8/3

2 1/3

miles/he.

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