Question

A steamer goes downstream and covers the distance between two ports in 3 hours. It covers the same distance in 5 hours when it goes upstream. If the stream flows at 3 km/hr, then find what is the speed of the steamer upstream​

Answer 1

$\large\underline{\sf{Given- }}$

• A steamer goes downstream and covers the distance between two ports in 3 hours.

• It covers the same distance in 5 hours when it goes upstream.

• The stream flows at 3 km/hr.

$\large\underline{\sf{To\:Find - }}$

• The speed of the steamer.

$\large\underline{\sf{Solution-}}$

Let assume that speed of the steamer be 'x' km per hour.

Speed of stream = 3 km per hour

Now,

• Speed of upstream = Speed of steamer - Speed of stream

So,

• Speed of upstream = x - 3 km per hour

Also,

• Speed of downstream = Speed of steamer + Speed of stream

So,

• Speed of downstream = x + 3 km per hour

Case :- 1

• Speed of downstream = x + 3 km per hour

• Time taken = 3 hours

We know,

$\green{\boxed{ \bf \: Distance = Speed \times Time}}$

Distance covered in 3 hours at the speed of (x + 3) km per hour is

$\rm :\longmapsto\:d_1 = 3 \times (x + 3)$

$\rm :\longmapsto\:d_1 = 3x + 9 - - - (1)$

Case :- 2

• Speed of upstream = x - 3 km per hour

• Time taken = 5 hours

So,

Distance covered in 5 hours at the speed of (x - 3) km per hour is

$\rm :\longmapsto\:d_2= 5(x - 3)$

$\rm :\longmapsto\:d_2= 5x - 15 - - - (2)$

According to statement,

Distance covered in upstream = Distance covered in downstream

$\bf\implies \:d_1 = d_2$

$\rm :\longmapsto\:3x + 9 = 5x - 15$

$\rm :\longmapsto\:3x - 5x = - 15 - 9$

$\rm :\longmapsto\: - 2x = - 24$

$\bf\implies \:x = 12 \:$

$\bf\implies \:Speed \: of \: the \: steamer = 12 \: km \: per \: hr$

Basic Concept Used :-

Writing System of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

Additional Information :

$\green{\boxed{ \bf \:Speed = \dfrac{Distance}{Time} }}$

$\green{\boxed{ \bf \:Time = \dfrac{Distance}{Speed} }}$