Question: At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in six hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this 24 mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour?
(A) 4/3
(B) 5/3
(C) 7/3
(D) 8/3
(E) 3/1
Correct Answer: D
Solution and Explanation
Approach Solution 1:
Let speed of current be c and speed of boat be b
Speed upstream = b – c
Speed downstream = b + c
12/(b−c) - 12/(b+c)= 6
b2 - c2= 4c - (i)
12/(2b−c) - 12/(2b+c)= 1
4b^2 - c^2= 24c - (ii)
Solving we get c = 8/3
Approach Solution 2:
Let the speed in still water be x mph and the speed of the current be y mph.
Speed of upstream= (x – y)
Speed of downstream= (x + y)
=> 12/x – y - 12/x + y= 6
=> 12x + 12y – 12x + 12y/x^2 – y^2= 6
=> 24y = 6(x^2-y^2)
=> x^2 – y^2 = 4y
=> x^2 = 4y + y^2….(1)
And, 12/(2x – y) - 12/(2x + y) = 1
=> 24x + 12y – 24x + 12y = 1(4x^2 - y^2)
=> 24y = (4x^2 – y^2)
=> x^2 = 24y + y^2/4….(2)
Now, comparing (1) and (2) we get,
=> 4y + y^2 = 24y + y^2/4
=> 16y + 4y^2 = 24y + y^2
=> 3y^2 = 8y
Therefore y= 8/3
The speed of the current is 8/3 mph
Approach Solution 3:
Given:
Downstream distance = 12 miles
Upstream distance= 12 miles
Time taken to travel downstream= 6 hrs less than upstream
Let the rowing rate of Rahul be “x” mph and rate of current be “y” mph
Then the speed in upstream and speed in downstream is given as:
Upstream Speed= (x−y)mph
Downstream speed= (x+y)mph
Distance= 12 miles
Time taken to travel 12 miles in upstream= 12/x−y
Time taken to travel 12 miles in downstream= 12/x+y
Then according to the question,
Time taken to travel in upstream - Time taken to travel in upstream = 6
12/x−y−12/x+y= 6
12(x+y)−12(x−y)/(x−y)(x+y)= 6
Perform a cross multiplication:
12(x+y)−12(x−y)= 6(x^2−y^2)
Simplify the equation:
24y= 6(x^2−y^2)
4y= x^2−y^2
x^2= y^2+4y… (1)
Now, it is given that Rahul doubles his speed, then his new speed becomes 2x mph.
Then the speed in upstream and speed in downstream is given as:
Upstream Speed= (2x−y) mph
Downstream speed= (2x+y) mph
Distance= 12 miles
Time taken to travel 12 miles in upstream= 12/2x−y
Time taken to travel 12 miles in downstream= 12/2x+y
Then according to the question,
Time taken to travel in upstream - Time taken to travel in upstream = 1
12/2x−y−12/2x+y=1
⇒ 12(2x+y)−12(2x−y)= 4x^2−y^2
⇒ 24y= 4x^2−y^2
⇒4x^2= y^2+24y… (2)
Substitute the value x^2 from the equation (1):
4(y^2+4y)= y^2+24y
4y^2+16y= y^2+24y
⇒ 3y^2= 8y
⇒3y= 8
⇒y= 8/3
So, the speed of the current is 8/3 mph.
“At his usual rowing rate, Rahul can travel 12 miles downstream in a”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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