Question

If I had walked 1 km per hour faster, I would have taken 10 minutes less to walk 2 km. Find the rate of my walking.​

Answer 1

$\huge\underline \mathbb {SOLUTION:-}$

$\mathsf {Distance = 2\:Km}$

$\mathsf {Let,\: Speed = x\:Km/hour}$

$\mathsf {New\:speed = (x + 1)\:Km/hour}$

$\mathsf {Time\:taken\:by\:normal\:speed = \frac{2}{x}hour}$

$\mathsf {Time\:taken\:by\:new\:speed = \frac{2}{x + 1}hour}$

$\underline \mathsf \red {According\:to\:question,}$

$\mathsf {\frac{2}{x} - \frac{2}{x + 1} = \frac{10}{60} }$

$\implies \mathsf {\frac{2x + 2 - 2x}{x^2 + x} = \frac{1}{6} }$

$\implies \mathsf {x^2 + x = 12}$

$\implies \mathsf {x^2 + x - 12 = 0}$

$\implies \mathsf {x^2 + 4x - 3x - 12 = 0}$

$\implies \mathsf {x(x + 4) - 3\:(x + 4) = 0}$

$\implies \mathsf {(x + 4)\:(x - 3) = 0}$

$\implies \mathsf {x = -4\:or\:x = 3}$

$\mathsf \blue {So,\:Speed\:is\:x = 3\:Km/hour}$

Answer 2

Answer:

\mathsf {Distance = 2\:Km}Distance=2Km

\mathsf {Let,\: Speed = x\:Km/hour}Let,Speed=xKm/hour

\mathsf {New\:speed = (x + 1)\:Km/hour}Newspeed=(x+1)Km/hour

\mathsf {Time\:taken\:by\:normal\:speed = \frac{2}{x}hour}Timetakenbynormalspeed=

x

2

hour

\mathsf {Time\:taken\:by\:new\:speed = \frac{2}{x + 1}hour}Timetakenbynewspeed=

x+1

2

hour

\underline \mathsf \red {According\:to\:question,}

Accordingtoquestion,

\mathsf {\frac{2}{x} - \frac{2}{x + 1} = \frac{10}{60} }

x

2

−

x+1

2

=

60

10

\implies \mathsf {\frac{2x + 2 - 2x}{x^2 + x} = \frac{1}{6} }⟹

x

2

+x

2x+2−2x

=

6

1

\implies \mathsf {x^2 + x = 12}⟹x

2

+x=12

\implies \mathsf {x^2 + x - 12 = 0}⟹x

2

+x−12=0

\implies \mathsf {x^2 + 4x - 3x - 12 = 0}⟹x

2

+4x−3x−12=0

\implies \mathsf {x(x + 4) - 3\:(x + 4) = 0}⟹x(x+4)−3(x+4)=0

\implies \mathsf {(x + 4)\:(x - 3) = 0}⟹(x+4)(x−3)=0

\implies \mathsf {x = -4\:or\:x = 3}⟹x=−4orx=3

\mathsf \blue {So,\:Speed\:is\:x = 3\:Km/hour}So,Speedisx=3Km/hour

Step-by-step explanation:

hope it will help you. .............