Question

Rahul can row downstream at 11 km/h and upstream at 7 km/h. Find the speed of Rahul in still water and the speed of the current.

• A. \(9 \text{ km/h} and 2 \text{ km/h}\)
• B. \(8 \text{ km/h} and 6 \text{ km/h}\)
• C. \(7 \text{ km/h} and 3 \text{ km/h}\)
• D. \(8 \text{ km/h} and 2 \text{ km/h}\)

Hint:

When solving problems involving motion in a river or stream, always consider the effects of the current by setting up equations for both downstream and upstream conditions.

Answer 1

The Correct Option is A

Determining the Speed of Rahul in Still Water and the Speed of the Current

Rahul's rowing speeds upstream and downstream are provided, which we use to calculate his speed in still water and the speed of the current. Let \( v \) be the speed of Rahul in still water and \( c \) the speed of the current. The downstream speed (\( v + c \)) is given as 11 km/h, and the upstream speed (\( v - c \)) is 7 km/h.

Using these speeds, we set up the following equations:

    v + c = 11  (downstream speed)
    v - c = 7   (upstream speed)
  

We can solve these equations simultaneously to find \( v \) and \( c \):

    v + c = 11
    v - c = 7
    Adding these equations, we get:
    2v = 18
    v = 18 / 2 = 9 km/h
  

Now substituting back to find \( c \):

    v + c = 11
    9 + c = 11
    c = 11 - 9 = 2 km/h
  

Thus, the speed of Rahul in still water is \( 9 \) km/h, and the speed of the current is \( 2 \) km/h. The answer corresponds to option (a).