Question

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

Answer 1

Answer:

8 km/h

Step-by-step explanation:

Speed of motorboat = 24 km/h

Distance = 32km

Let the speed of stream be = x

Time taken by motorboat to go upstream = 32/(24-x)

Time taken by motorboat to go downstream= 32/(x+ 24)

Thus,

= 32/(x+24) + 1 = 32/(24- x)

=32/(24- x) - 32/(x+24) = 1

=32(x+24) - 32(24-x) = (24-x)(x+24)

=32x + (32×24 - 32×24) + 32x = 242 - x²

= 64x = 576 - x²

= x² +64x - 576 = 0

= x² +72x - 8x -576 = 0

= x(x+72) - 8(x-72) =0

= x -8 = 0 or x+72=0

= x = 8km/h as x can not be negative = -72

Thus, the speed of stream is 8km/h.

Answer 2

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

Solution:

Let,

Speed of stream = x km/h

Speed of boat towards upstream =

(24−x)km/hr

Speed of boat toward upstream =

(24+x)km/hr .

It is given that,

Distance covered = 32 km

Time taken for upstream journey :-

$\red\bf\green{Time\:=\:\dfrac{32}{24\:-\:x}\:hrs\:}$

hrs ----(1)

Time taken for downstream journey :-

$\red\bf\green{Time\:=\:\dfrac{32}{24\:+\:x}\:hrs\:}$

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);

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

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

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

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

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

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

:⟹x(x+72)−8(x+72)=0

:⟹(x+72)(x−8)=0

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

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

NOTE :- Speed never be negative .

$\begin{gathered}\\ \\\end{gathered}$

$\begin{gathered}\bf{:\implies\:x\:=\:8\:km/hr\:}\\ \\\end{gathered}$

∴ The speed of the stream is "8 km/hr"