A boat goes 21 km upstream and 18 km downstream in 9 hours. In 13 hours, it can go 30 km upstream and 27 km downstream. Determine the speed of the stream and that of the boat in still water. (Speed of boat in still water is more than the speed of the stream of river.)

Let the speed of the boat in still water be x km/hr and the speed of stream be y km/hr. It is necessary that x > y.

The speed of the boat in downstream = (speed of boat in still water + speed of stream) = (x + y) km/hr.

The speed of boat in upstream = (speed of boat in still water – speed of stream) = (x – y) km/hr.

Also, we know that

In the first case, it is given that boat goes 21 km upstream and 18 km downstream in 9 hours

Time taken by boat in upstream and downstream = 9 hr

In the second case, it is given that boat goes 30 km upstream and 27 km downstream in 13 hours

Time taken by boat in upstream and downstream = 13 hr

Putting these value in (i) and (ii), we get

21a + 18b = 9

30a + 27b = 13

So, the given equations transforms into linear equation in two variables

7a + 6b = 3 …. (iii)

30a + 27b = 13 … (iv)

Multiply (iii) by 9 and (iv) by 2,

63a + 54b = 27 …. (v)

60a + 54b = 26 … (vi)

Subtract (vi) from (v),

63a + 54b – 60a – 54b = 27 – 26

3a = 1

Putting above value in (iii),

… (vii)

…. (viii)

x – y + x + y = 3 + 9

2x = 12

x = 6

Putting x = 6 in (viii),

y = 9 – 6

y = 3

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Pair of Linear Equations in Two Variables46 mins
Dealing With the Real Life Problems53 mins
Learn to Solve Real Life Problems Using Linear Equations in Two Variables36 mins
Quiz | Real Life Problems Through Linear Equations56 mins
Quiz | Solution of Linear Equations53 mins
Champ Quiz | Consistency and Inconsistency of Solutions36 mins
Emphasizing on Elimination Method48 mins
Elimination (quicker than quickest)44 mins
Consistent and Inconsistent Equations33 mins
Algebraic Methods to Solve Pair of Linear Equation44 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses