Question

a car moves at a distanceof 400km at a certain speed had the speed been 12 km per hour more the time taken for the journey would have been 1 hr 40 min less find the original speed pls full sol​

Answer 1

Answer:

Step-by-step explanation:

Solution :-

Let the original speed of car be x km/h.

We know that,

Time = Distance/Time

t = 400/x

Increased speed = (x + 12) Km/h

According to the Question,

⇒ 400/x - 400/x + 12 = 1(40/60)

⇒ 400x + 4800 - 400x/x(x + 12) = 1(2/3)

⇒ 4800/x(x + 12) = 5/3

⇒ 5x² + 60x - 14400 = 0

⇒ x² + 12x - 2880 = 0

⇒ x² + 60x - 48x - 2880 = 0

⇒ x(x + 60) - 48(x + 60) = 0

⇒ (x + 60) (x - 48) = 0

⇒ x = - 60 or 48 (Neglecting negative sign)

⇒ x = 48 km/h

Hence, the original speed is 48 km/h.

Answer 2

Answer:

• Fixed Distance = 400 km
• Let Original Speed = n km/hr
• New Speed will be = (n + 12) km/hr
• Time Taken = 1hr 40 min. Less

$\bf{\dag}\:\boxed{\sf Time=\dfrac{Distance}{Speed}}$

$\rule{150}{1}$

$\underline{\bigstar\:\:\textsf{According to the Question :}}$

$\dashrightarrow\tt\:\:Time_1-Time_2 = 1 hr.\:40 min.\\\\\\\dashrightarrow\tt\:\:</p><p>\dfrac{Distance}{Speed_1}-\dfrac{Distance}{Speed_2}=1hr+{}^{40}\!/{}_{60}hr\\\\\\\dashrightarrow\tt\:\:\dfrac{400}{n}-\dfrac{400}{(n+12)}=1{}^{2}\!/{}_{3}hr\\\\\\\dashrightarrow\tt\:\:400\bigg[\dfrac{1}{n}-\dfrac{1}{(n+12)}\bigg]=\dfrac{5}{3}\\\\\\\dashrightarrow\tt\:\:80\bigg[\dfrac{n+12-n}{n(n+12)}\bigg]=\dfrac{1}{3}\\\\\\\dashrightarrow\tt\:\:\dfrac{12}{n^2+12n}=\dfrac{1}{80\times3}\\\\\\\dashrightarrow\tt\:\:\dfrac{12}{n^2+12n}=\dfrac{1}{240}\\\\\\\dashrightarrow\tt\:\:240(12)=n^2+ 12n\\\\\\\dashrightarrow\tt\:\:2880 = n^2 + 12n\\\\\\\dashrightarrow\tt\:\:n^2+ 12n - 2880 = 0\\\\\\\dashrightarrow\tt\:\:n^2+ (60 - 48)n - 2880 = 0\\\\\\\dashrightarrow\tt\:\:n^2 + 60n - 48n - 2880 = 0\\\\\\\dashrightarrow\tt\:\:n(n + 60) - 48(n + 60) = 0\\\\\\\dashrightarrow\tt\:\:(n - 48)(n + 60) = 0\\\\\\\dashrightarrow\:\:\underline{\boxed{\tt\green{n=48\:km/hr}\quad\tt or\quad\red{n=-\:60\:km/hr}}}$

⠀

$\therefore\:\underline{\textsf{Original Speed of the car is \textbf{48 km/hr}}}.$