Question

A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.​

Answer 1

✬ Speed = 8 km/h ✬

Step-by-step explanation:

Given:

• Speed of motorboat is 24 km/h.
• Boat takes 1 hour more to go 32 km upstream than to return downstream to the same spot.

To Find:

• What is the speed of stream ?

Solution: Let the speed of the stream be x km/h. Therefore,

➟ Speed of boat upstream = (24 – x) km/hr

➟ Speed of boat downstream = (24 + x) km/h

As we know that

★ Time = Distance/Speed ★

➟ Time for covering 32 km in upstream will be

• 32/(24 – x) hours

➟ Time for covering 32 km in downstream will be

• 32/(24 + x) hours

Now, A/q

• Boat takes 1 hour more to go 32 km upstream than to return downstream to the same spot.

➮ 32/(24 – x) – 32/(24 + x) = 1

➮ 32[(24 + x) – (24 – x)] = (24 – x) (24 + x)

➮ 32(24 + x – 24 + x) = 24² – x²

➮ 32(2x) = 576 – x²

➮ 64x = 576 – x²

➮ x² + 64x – 576 = 0

Now by middle term splitting method.

➮ x² + 72x – 8x – 576 = 0

➮ x(x + 72) – 8(x + 72) = 0

➮ (x – 8) or (x + 72) = 0

➮ x = 8 or x = – 72

We will neglect the negative value of x because speed cannot be negative.

Hence, speed of stream is 8 km/h

Answer 2

$\huge{\underbrace{\gray{GIVEN:-}}}$

• The speed of a motor boat in still water is 24 km/h .

• The boat takes 1 hour more to go 32 km upstream than to return downstream to the same spot .

$\huge{\underbrace{\gray{TO\:FIND:-}}}$

• The speed of the stream .

$\huge{\underbrace{\gray{SOLUTION:-}}}$

Let,

• $\bf\red{Speed\:of\:stream}$ = x km/h

✫ Speed of boat towards upstream = $\bf\blue{(24\:-\:x)\:km/hr}$ .

✫ Speed of boat towards downstream = $\bf\blue{(24\:+\:x)\:km/hr}$ .

☞︎︎︎ It is given that,

• $\bf\red{Distance\:covered}$ = 32 km

Time taken for upstream journey :-

$\huge\red\checkmark$ $\bf\purple{Time\:=\:\dfrac{32}{24\:-\:x}\:hrs\:}$----(1)

Time taken for downstream journey :-

$\huge\red\checkmark$ $\bf\purple{Time\:=\:\dfrac{32}{24\:+\:x}\:hrs\:}$----(2)

• It is given that, The boat takes 1 hour more to go 32 km upstream than to return downstream to the same spot .

☯︎ Now, Equation (1) - Equation (2);

$\rm{:\implies\:\:\dfrac{32}{24\:-\:x}\:-\:\dfrac{32}{24\:+\:x}\:=\:1\:}$

$\rm{:\implies\:\:\dfrac{1}{24\:-\:x}\:-\:\dfrac{1}{24\:+\:x}\:=\:\dfrac{1}{32}\:}$

$\rm{:\implies\:\:\dfrac{24\:+\:x\:-\:24\:+\:x}{(24)^2\:-\:x^2}\:=\:\dfrac{1}{32}\:}$

$\rm{:\implies\:\:(24)^2\:-\:x^2\:=\:64x\:}$

$\rm{:\implies\:\:x^2\:+\:64x\:-\:576\:=\:0\:}$

$\rm{:\implies\:\:x^2\:+\:72x\:-\:8x\:-\:576\:=\:0\:}$

$\rm{:\implies\:\:x\:(x\:+\:72)\:-8\:(x\:+\:72)\:=\:0\:}$

$\rm{:\implies\:\:(x\:+\:72)\:(x\:-\:8)\:=\:0\:}$

$\rm{:\implies\:\:x\:+\:72\:=\:0\:\:\:\:\:or\:\:\:\:\:\:x\:-\:8\:=\:0\:}$

$\rm{:\implies\:\:x\:=\:-72\:\:\:\:\:or\:\:\:\:\:\:x\:=\:8\:}$

[NOTE :- Speed never be negative .]

$\bf\green{:\implies\:x\:=\:8\:km/hr\:}$

$\red\therefore$ The speed of the stream is "8 km/hr" .