Question

A boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours it can go 40km

upstream and 5.5km down stream. Determine the speed of the stream and that of the boat

in still water.​

Answer 1

Correct Question :- A boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours it can go 40km

upstream and 55km down stream. Determine the speed of the stream and that of the boat in still water. ?

Concept used :-

• Downstream Speed = (Speed of Boat in Still water + Speed of Water in The river).
• Upstream Speed = (Speed of Boat in Still water - Speed of Water in The river).
• Time = (Distance/Speed).

Solution :-

Let us Assume That, Speed of Boat in still water is xkm/h & speed of current is y km/h.

Than,

→ Downstream Speed = (x + y) km/h.

→ Upstream Speed = (x - y) km/h.

Now,

Case (1) :-

→ 30km upstream + 44km Downstream = 10 Hours.

→ 30/(x - y) + 44/(x + y) = 10

Let 1/(x - y) = u & 1/(x + y) = v

So,

→ 30u + 44v = 10 ------------ Equation (1).

______________

Case (2) :-

→ 40 km upstream + 55 km Downstream = 13 Hours.

→ 40/(x - y) + 55/(x + y) = 13

Let 1/(x - y) = u & 1/(x + y) = v

So,

→ 40u + 55v = 13 ------------ Equation (2).

_______________

Multiply Equation (1) by 4 and Equation (2) by 3 , and Than subtracting Equation (1) From Equation (2) , we get,

→ 4(30u + 44v) - 3(40u + 55v) = 4*10 - 3*13

→ 120u - 120u + 176v - 165v = 40 - 39

→ 11v = 1

→ v = (1/11)

Putting Value of v in Equation (2) Now, we get,

→ 40u + 55*(1/11) = 13

→ 40u + 5 = 13

→ 40u = 13 - 5

→ 40u = 8

→ u = (8/40)

→ u = (1/5).

________________

Putting Back These values we get :-

→ 1/(x - y) = (1/5)

→ (x - y) = 5 ------------- Equation (3).

And,

→ 1/(x + y) = (1/11)

→ (x + y) = 11 ------------ Equation (4).

_________________

Adding Equation (3) & (4) Now, we get,

→ (x - y) + (x + y) = 5 + 11

→ 2x = 16

→ x = 8km/h.. (Ans.)

Putting This value in Equation (3) now,

→ 8 - y = 5

→ y = 8 - 5

→ y = 3km/h..(Ans.)

Hence, Speed of Boat in Still water is 8km/h & Speed of current is 3km/h.

Answer 2

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$\huge\tt{GIVEN:}$

• A boat goes 30km upstream and 44km downstream in 10 hours.
• In 13 hours it can go 40km upstream and 55km down stream.

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$\huge\tt{TO~FIND:}$

• Determine the speed of the stream and that of the boat

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$\huge\tt{SOLUTION:}$

Let the Speed of Boat in still water be xkm/h & speed of current be y km/h.

Than,

↪ Downstream Speed = (x + y) km/h.

↪Upstream Speed = (x - y) km/h.

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Firstly,

↪ 30km upstream + 44km Downstream = 10 Hours

↪30/(x - y) + 44/(x + y) = 10

↪Let 1/(x - y) = u & 1/(x + y) = v

So,

↪30u + 44v = 10 _____(EQ.1)

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Sencondly,

↪ 40 km upstream + 55 km Downstream = 13 Hours.

↪40/(x - y) + 55/(x + y) = 13

↪Let 1/(x - y) = u & 1/(x + y) = v

So,

↪ 40u + 55v = 13 ______(EQ.2)

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Multipling EQ.1 by 4 and EQ.2 by 3 , and Than subtracting EQ.1 from EQ.2

↪ 4(30u + 44v) - 3(40u + 55v) = 4*10 - 3*13

↪ 120u - 120u + 176v - 165v = 40 - 39

↪ 11v = 1

↪v = (1/11)

Putting Value of v in EQ.2

↪40u + 55*(1/11) = 13

↪ 40u + 5 = 13

↪40u = 13 - 5

↪ 40u = 8

↪ u = (8/40)

↪ u = (1/5)

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Putting The values back,

↪ 1/(x - y) = (1/5)

↪ (x - y) = 5 _____(EQ.3)

And,

↪1/(x + y) = (1/11)

↪ (x + y) = 11 _______(EQ.4)

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Adding (EQ.3 & 4) Now, we get,

↪ (x - y) + (x + y) = 5 + 11

↪ 2x = 16

↪ x = 8km/hr

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Putting This value in (EQ.3),

↪8 - y = 5

↪ y = 8 - 5

↪ y = 3km/hr

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