Question

A boat goes downstream and covers a distance in 5 hours, while its cover the same distance upstream in 8 hours. if the speed of the stream is 3 km/hr . find the speed of the boat in still water.​

Answer 1

Answer :-

★ Concept :-

Here the concept Linear Equations in Two Variable has been used. According to this, if we make the value of variable depend on constants, we can find the value of it. The standard form of Linear Equations in One Variable is given as :-

ax + b = 0

• Distance = Speed × Time

___________________________

★ Question :-

A boat goes downstream and covers a distance in 5 hours, while its cover the same distance upstream in 8 hours. If the speed of the stream is 3 km/hr . Find the speed of the boat in still water.

★ Solution :-

Given,

» Time taken to cover the distance while going upstream = 5 hours.

» Time taken to cover the distance while going downstream = 8 hours.

✏ Let the speed of the stream be 's' km/hr.

✏ Let the distance between the two ports be 'x' Km.

Now,

=> Speed of boat while upstream = (s - 3) Km/hr

=> Speed of boat while downstream = (s + 3) Km/hr

Now according to the question,

~ Case I (For downstream journey) :-

➥ x = 5(s + 3)

➥ x = 5s + 15 ... (i)

________________________________

~ Case II (For upstream journey) :-

➥ x = 8 × (s - 3)

➥ x = 8s - 24 ... (ii)

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

➫ 5s + 15 = 8s - 24

➫ 8s - 5s = 15 + 24

➫ 3s = 39

$\: \: \therefore \: \: \huge{\bf{s \: = \: \dfrac{39}{3}}}$

➫ s = 13

$\:\:\:\underline{\boxed{\sf{\red{Hence, \: speed \: of \: the \: boat \: is \: \underline{13 \: Km/hr} \:}}}}$

___________________________

Now using, equation (i) and the value of s, we get,

➠ x = 5s + 15

➠ x = 5(13) + 15

➠ x = 65 + 15

➠ x = 80 Km

$\:\:\:\underline{\boxed{\sf{\blue{Hence, \: distance \: between \: the \: places \: is \: \underline{80 \: Km} \:}}}}$

______________________________

$\: \: \: \boxed{\rm{\green{Confused \: ? \: Don't \: worry, \: let's \: verify \: it \:}}}$

For verification we need to simply apply the values we got, into any of the equation we formed. Let us take both equations :-

~ Case I -

✒ x = 5s + 15

✒ 80 = 5(13) + 15

✒ 80 = 65 + 15

✒ 80 = 80

Clearly, LHS = RHS.

~ Case II -

✒ x = 8s - 24

✒ x = 8(13) - 24

✒ 80 = 65 + 39 - 24

✒ 80 = 80

Clearly, LHS = RHS.

Here both the situations are satisfied, hence our answer is correct.

________________________

$\: \: \: \underline{\boxed{\rm{\orange{Refer \: to \: supplementary \: artefacts \:}}}}$

• Linear Equations are the set of constants and variables joined such that when we apply the value of variable and use algebraic signs, the result should be zero.

• Linear Equations in Two Variables are the equations where we have to find the value of two different variables simultaneously using constant terms. Standard form is given as :-

ax + by + c = 0

px + qy + r = 0

Answer 2

Given,

• Time taken to cover a distance in downstream = 5 h

• Time taken to cover same distance in upstream = 8 h

• Speed of stream = 3 km/h

To find,

• Speed of boat in still water

Solution :

Let the speed of boat in still water be x km/h

We know,

Distance =  Speed * Time

Now as we know in downstream, speed of stream will be added to speed of boat in still water.

⇒ Distance (downstream) = (x + 3) * 5

⇒ Distance (downstream) = 5(x + 3) km

And in upstream, speed of stream will be subtracted from speed of boat in still water.

⇒ Distance (upstream) = (x - 3) * 8

⇒ Distance (upstream) = 8(x - 3) km

Now according to question,

⇒ 5(x + 3) = 8(x - 3)

⇒ 5x + 15 = 8x - 24

⇒ 5x - 8x = -24 -15

⇒ -3x = -39

⇒ x = -39/-3

⇒ x = 13 km/h

∴ Speed of boat in still water = 13 km/h