Question

The difference of the car of a faster car and a slower car is a 20 km per hour is the slower car takes 1 hour more than the faster car to travel a distance of 400 km find speed of both the cars

Answer 1

Step-by-step explanation:

Let the speed of the slower car be x

Let the faster car be x+20

Distance=400km

Time taken by slower car - time taken by faster car= 1 hour

400/x - 400/x+20= 1

(x+20) 400 - 400x/ x( x+20 )= 1

400x + 8000 - 400x = x sq. + 20x

x sq. + 20x = 8000

x sq. + 20x - 8000 = 0

x sq. + 100x - 80x - 8000= 0

x(x + 100) - 80 (x + 100)= 0

(x - 80) (x + 100)= 0

x - 80 = 0

x = 0 + 80

therefore, x = 80 and x + 100=0

x=0-100

therefore x = -100 not possible

Hence,the speed of slower car is 80 km/hr

and the speed of faster car is 100 km/hr

Answer 2

Answer:

The Speed of faster car is 40 km/h

The Speed of slower car is 20 km/h  

Step-by-step explanation:

Given as :

The total distance = d = 400 km

Let The speed of faster car = S km/h

The speed of slower car = s km/h

And The difference between the speed of car = (S - s) km/h = 20 km/h

The time taken by faster car = t hours

The slower car take one hour more than faster car

So, The time taken by slower car =( t + 1 ) hour

According to question

Distance = speed × time

For faster car

d = S × t

Or, 400 = S t  

i.e t = $\dfrac{400}{S}$          .......1

For slower car

time = $\dfrac{400}{S-20}$

Since time taken by slower car is 1 hour more

So, t + 1 = $\dfrac{400}{S-20}$

Or, $\dfrac{400}{S}$ + 1 = $\dfrac{400}{S-20}$

Or, $\dfrac{400}{S-20}$ - $\dfrac{400}{S}$ = 1

Or, 400 S - 400 (S - 20) = S (S - 20)

Or, 400 S - 400 S + 8000 = S² - 20 S

Or, 0 + 8000 = S² - 20 S

Or, S² - 20 S - 8000 = 0

Solving the equation

i.e S² - 40 S + 20 S - 8000 = 0

Or, S (S - 40 ) + 20 (S - 40) = 0

i.e (S - 40 ) ( S + 20) = 0

∴   S = 40 km/h   , S = - 20

So, The Speed of faster car = S = 40 km/h

And The Speed of slower car = S - 20 = 40 - 20 = 20 km/h

Hence, The Speed of faster car is 40 km/h

And The Speed of slower car is 20 km/h  Answer