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Pair of Linear Equations in Two Variables | Pair of Linear Equations in Two Variables - Exercise 3.4

Question 6

A person, rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.

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Let the speed of the stream be x km/hr.

And, the speed of the boat in still water = 5 km/hr

Speed of the boat upstream = (5 – x)km/hr

Speed of the boat downstream = (5 + x) km/hr

Time taken in rowing 40 km upstream = 40/(5-x) hrs

Time taken in rowing 40 km downstream = 40/(5+x) hrs

According to the question, we have

Time taken in 40 km upstream = 3 × Time taken in 40 km downstream

\therefore \frac{40}{5-x}=\frac{3 \times 40}{5+x} \\ \Rightarrow \frac{1}{5-x}=\frac{3}{5+x} \\ \Rightarrow-3 x+15=x+5 \\ \Rightarrow-3 x-x=5-15 \\ \Rightarrow-4 x=-10 \\ \Rightarrow x=\frac{10}{4}

⇒ x = 2.5 km/hr

Hence, the speed of stream is 2.5 km/hr.

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Question 6

A person, rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

Let the speed of the stream be x km/hr.

And, the speed of the boat in still water = 5 km/hr

Speed of the boat upstream = (5 – x)km/hr

Speed of the boat downstream = (5 + x) km/hr

Time taken in rowing 40 km upstream = 40/(5-x) hrs

Time taken in rowing 40 km downstream = 40/(5+x) hrs

According to the question, we have

Time taken in 40 km upstream = 3 × Time taken in 40 km downstream

\therefore \frac{40}{5-x}=\frac{3 \times 40}{5+x} \\ \Rightarrow \frac{1}{5-x}=\frac{3}{5+x} \\ \Rightarrow-3 x+15=x+5 \\ \Rightarrow-3 x-x=5-15 \\ \Rightarrow-4 x=-10 \\ \Rightarrow x=\frac{10}{4}

⇒ x = 2.5 km/hr

Hence, the speed of stream is 2.5 km/hr.

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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