Question

A boat can travel 6 km downstream in 40 minutes. The return trip requires an hour. Find the rate of the boat in still water and the rate of the current.

Answer 1

||✪✪ QUESTION ✪✪||

A boat can travel 6 km downstream in 40 minutes. The return trip requires an hour. Find the rate of the boat in still water and the rate of the current. ?

|| ★★ CONCEPT USED ★★ ||

if Speed of boat in x km/h , and speed of current is y km/h , Than :-

→ Speed in Downstream = (x + y) km/h .

→ Speed in Upstream = (x - y) km/h.

Also , Time = (Distance / Speed ) .

→ 1 hour = 60 Minutes .

|| ✰✰ ANSWER ✰✰ ||

Let us assume That Speed of boat in Still water is x km/h , and speed of current is y km/h .

So, we can say That :-

→ 6/(x + y) = 40 min . = 40/60 = (2/3) hours.

Cross - Multiply,

→ 2(x + y) = 6*3

→ (x + y) = 9 ------------ Equation (1).

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Also,

→ 6/(x - y) = 1

→ (x - y) = 6 . ------------ Equation (2).

__________________

Adding both Equations We get,

→ (x + y) + (x - y) = 9 + 6

→ 2x = 15

Dividing both sides by 2

→ x = 7.5km/h.

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Putting This value in Equation (1) we get,

→ 7.5 + y = 9

→ y = 9 - 7.5

→ y = 1.5km/h.

Hence, Speed of the boat in still water is 7.5km/h and the rate of the current is 1.5km/h.

Answer 2

Given: A boat can travel 6 km downstream in 40 minutes and return back upstream in an hor [60 minutes].

To find: The speed of the boat and the current.

Answer:

Let the speed of the boat be x km/h and that of the current be y km/.

This implies that:

• x + y = [downstream]
• x - y = [upstream]

We know that speed =  $\tt \frac{Distance}{Time}$.

Therefore, according to the question,

$\tt \dfrac{6}{x\ -\ y}\ =\ 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [Equation\ 1]\\\\\\\dfrac{6}{x\ +\ y}\ =\ \dfrac{40}{60}\ =\ \dfrac{2}{3}\ \ \ \ \ \ \ \ [Equation\ 2]$

Equation 1 ⇒ x - y = 6.

Equation 2 ⇒ x + y = 2x + 2y = 18 ⇒ x + y = 9.

On solving the equations, we get x = 7.5 and y = 1.5.

Therefore, the speed of the boat in still water is 7.5 km/h and speed of the current is 1.5 km/h.