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.

Suggested GMAT Problem Solving Samples

• John is 20 years older than Brian. 12 years ago, John was twice as old GMAT Problem Solving
• A Train Overtakes Two Persons Who Are Walking In The Same Direction GMAT Problem Solving
• If 1/x − 1/x+1= 1/x+4, Then x could be GMAT Problem Solving
• If x = - |x|, Then Which One of the Following Statements GMAT Problem Solving
• A Bag Contains 4 Red and 3 Black Balls. A Second Bag Contains 2 Red GMAT Problem Solving
• A Mixture of 40 Litres of Milk and Water, Contains 20% of Water GMAT Problem Solving
• A Candidate is Required to Answer 6 Out of 10 Questions Divided into 2 Groups GMAT Problem Solving
• Company XYZ had $498.2 Million in Profits for the Year GMAT Problem Solving
• If -2 < a < 11 and 3 < b < 12, Then Which of the Following is NOT Always True GMAT Problem Solving
• Karan and Arjun run a 100-metre Race, Where Karan Beats Arjun by 10 metres GMAT Problem Solving
• The Figure below Shows an Equilateral Triangle ABC Tangent GMAT Problem Solving
• Three groups of children contain respectively 3 girls and 1 boy GMAT Problem Solving
• If x=10^{10},\frac{x^2+2x+7}{3x^2-10x+200} is closest to GMAT Problem Solving
• If set S Consists of all Different Solutions of Equation |x – 4| = x, What is the Range of Set S GMAT Problem Solving
• Set T consists of all points (x, y) such that \(x^2+y^2=1\) GMAT Problem Solving
• How Many Natural Numbers Not Exceeding 4321 can be Formed GMAT Problem Solving
• If the Perimeter of Square Region S and the Perimeter of Rectangular GMAT Problem Solving
• If x^9= 9^9^9, What is the Value of x? GMAT Problem Solving
• In a Competition, a School Awarded Medals in Different Categories GMAT Problem Solving
• In how many ways can 5 apples (identical) be distributed among 4 children? GMAT problem solving
• What is Greatest Positive Integer n such that 2^n is a Factor of 12^10? GMAT Problem Solving
• All the five digit numbers in which each successive digit exceeds its GMAT Problem Solving
• A box contains two white balls, three black balls and four red balls GMAT Problem Solving
• Consider An Obtuse-Angled Triangles With Sides 8 Cm, 15 Cm GMAT Problem Solving
• I Travel The First Part Of My Journey At 40 Miles Per Hour GMAT Problem Solving
• Profit Earned By Selling An Article At 1060 Is 20 % More Than The Loss GMAT Problem Solving
• A Perfect Square is a Number that Becomes an Integer when Square GMAT Problem Solving
• If x + y = 2 and x^2 + y^2 = 2, What is the Value of xy? GMAT Problem Solving
• The Owner of A Local Jewellery Store Hired 3 Watchmen to Guard his Diamonds GMAT Problem Solving
• What is the smallest integer n for which 25^n>5^12 GMAT Problem Solving
• Ten Coins are Tossed Simultaneously. In how many of the Outcomes GMAT Problem Solving
• If x^2 − 2 < 0, which of the following specifies all the possible GMAT Problem Solving
• The Mass Of 1 Cubic Meter Of A Substance Is 800 Kilograms GMAT Problem Solving
• A Dairyman Pays Rs. 6.40 Per Liter Of Milk GMAT Problem Solving
• A Train Approaches A Tunnel AB. Inside The Tunnel Is A Cat Located GMAT Problem Solving
• In an Isosceles Triangle PQR, If ∠Q = 80 Degrees, Then What is The GMAT Problem Solving
• Two Members of a Club are to be Selected to Represent the Club GMAT Problem Solving
• The Square Root of 24336 is Exactly GMAT Problem Solving
• A Certain Purse Contains 30 Coins, Each Coin is either a Nickel or GMAT Problem Solving
• Which of the Following is Equal to the Value of 2^5+2^5+3^5+3^5+3^5 ? GMAT Problem Solving
• The Price of a Certain Painting Increased By 20% During the First Year GMAT Problem Solving
• Machine A Produces 100 Parts Twice as Fast as Machine B does GMAT Problem Solving
• The Difference Between a Two-Digit Number and the Number Obtained GMAT Problem Solving
• Which of the following is always equal to sqrt(9+x^2-6x)?GMAT Problem Solving
• A Colony has Houses Numbered 1 to 150 GMAT Problem Solving
• Two Vessels A and B Contain Milk and Water Mixed in the Ratio 8:5 GMAT Problem Solving
• A Dealer Offers a Cash Discount of 20%. Further, a Customer Bargains GMAT Problem Solving
• If a Regular Hexagon is Inscribed in a Circle with a Radius of 4, The GMAT Problem Solving
• There are Two Vessels A and B. Vessel A is Containing 40 Litres of GMAT Problem Solving
• At A Certain Fruit Stand, The Price Of Each Apple Is 40 Cents GMAT Problem Solving