Question

form the linear equations in the following problems and find their solutions by any algebraic method ​

Answer 1

Answer:

60 and40 km/hr

Step-by-step explanation:

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thanked me if correct

Answer 2

Given :

• Places A and B are 100 km apart.
• Both the cars start at the same time.
• When both cars travel in same direction at different speed, they meet after 5 hrs.
• If they travel towards each other they meet in 1 hr.

To Find :

• Speed of cars.

Solution :

Let the speed of car A be x km/hr.

Let the speed of car B be y km/hr.

Case 1 :

✪ When, two bodies travel in same direction the relative speed is the difference between the speed of two bodies.

Distance between places A and B is 100 km.

Time taken →5 hrs

Formula :

$\large{\boxed{\mathtt{\red{Speed\:={\dfrac{Distance}{Time}}}}}}$

$\longrightarrow$ $\mathtt{Speed\:=\:{\dfrac{100}{5}}}$

$\longrightarrow$ $\mathtt{Speed\:=\:20\:km\:per\:hr}$

Relative speed between the two car is 20 km/hr.

Equation :

$\mathtt{x-y=20}$ _____(1)

Case 2 :

✪ When, two bodies travel towards each other, the relative speed is the sum of speeds between the two bodies.

Distance : 100 km.

Time → 1 hr

Using the formula for speed,

$\longrightarrow$ $\mathtt{Speed\:=\:{\dfrac{100}{1}}}$

$\longrightarrow$ $\mathtt{Speed\:=\:100\:km\:per\:hr}$

Equation :

$\mathtt{x+y\:=\:100}$ ____(2)

✪ Solve equation 1 and equation 2 to find value of x and y.

Add equation 1 to equation 2,

$\longrightarrow$ $\mathtt{x-y\:+\:x+y\:=\:100\:+\:20}$

$\longrightarrow$ $\mathtt{2x\:=\:120}$

$\longrightarrow$ $\mathtt{x\:=\:{\dfrac{120}{2}}}$

$\longrightarrow$ $\mathtt{x=60}$

$\large{\boxed{\sf{\red{Speed\:of\:car\:A\:=\:60\:kmph}}}}$

✪ Substite x = 60 in equation 1,

$\longrightarrow$ $\mathtt{x-y\:=\:20}$

$\longrightarrow$ $\mathtt{60-y=20}$

$\longrightarrow$ $\mathtt{-y=20-60}$

$\longrightarrow$ $\mathtt{-y=-40}$

$\longrightarrow$ $\mathtt{y=40}$

$\large{\boxed{\sf{\red{Speed\:of\:car\:B\:=\:40\:kmph}}}}$