Name: Condition of Solvability
Uploaded: 2019-07-19
Duration: 8 min 45 s
Description: In this video, we discuss the relation between the coefficients of a pair of linear equations in two variables. Watch this video and explore the concept.

Question

A motorboat can travel

30 km

upstream and

28 km

downstream in

7 hours

. It can travel

21 Km

upstream and return in

5 hours

. Find the speed of the boat in still water and the speed of the stream.

Accepted Answer

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

Let the speed of stream be $y km / hr$

Therefore, Speed of boat upstream $= (x - y) km / hr$

Speed of boat downstream $= (x + y) km / hr$

We know that,

$time = \frac{distance}{speed}$

Given,

Boat can travel $30 km$ upstream and $28 km$ downstream in $7 hours$ .

Also, Boat can travel $21 km$ upstream and return in $5 hours$ .

$\Rightarrow \frac{30}{x - y} + \frac{28}{x + y} = 7 . . . . (i)$

And, $\frac{21}{x - y} + \frac{21}{x + y} = 5 \dots (i i)$

Let,

$\frac{1}{x + y} = u & \frac{1}{x - y} = v \Rightarrow 28 u + 30 v = 7 . . . (iii) 21 u + 21 v = 5 . . . . (iv)$

Multiply $(iii)$ by $21$ and $(iv)$ by $30$ , we get

$588 u + 630 v = 147 . . . . (v) 630 u + 630 v = 150 . . . . (vi)$

Subtracting $(v)$ from $(vi)$ , we get

$42 u = 3 u = \frac{3}{42} = \frac{1}{14}$

Substituting $u$ value in $(iv)$ , we get,

$21 v + 21 (\frac{1}{14}) = 5 21 v = 5 - \frac{3}{2} 21 v = \frac{7}{2} v = \frac{1}{6}$

Now,

$u = \frac{1}{x + y} & v = \frac{1}{x - y} \frac{1}{14} = \frac{1}{x + y} & \frac{1}{6} = \frac{1}{x - y} \Rightarrow x + y = 14 . . . . (v ii) x - y = 6 . . . . (viii)$

Adding $(vii) & (viii)$ , we get,

$2 x = 20 x = 10$

Substituting $x$ value in $(vii)$ , we get

$10 + y = 6 y = 4$

Therefore, speed of boat in still water is $10 km / hr$ and speed of stream is $4 km / hr$ .

A motorboat can travel $30 km$ upstream and $28 km$ downstream in $7 hours$ . It can travel $21 Km$ upstream and return in $5 hours$ . Find the speed of the boat in still water and the speed of the stream.

Important Questions on Pair Of Linear Equations In Two Variables

Learn and Prepare for any exam you want !

A motorboat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 Km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.

Important Questions on Pair Of Linear Equations In Two Variables

Learn and Prepare for any exam you want !

A motorboat can travel $30 km$ upstream and $28 km$ downstream in $7 hours$ . It can travel $21 Km$ upstream and return in $5 hours$ . Find the speed of the boat in still water and the speed of the stream.