The westbound bus headed for a town at a speed that was 40 kilometers per hour slower than the speed of a car traveling eastbound towards the town. The speed of the car was 120 kilometers per hour. Though both vehicles spent the same time traveling, the car traveled 20 kilometers more than the bus. How long did each of the vehicles travel?

The bus =40 kilometers

The car = 60km

Step-by-step explanation:

step one:

given

The speed of the car was 120  kilometers per hour

The speed of the bus is 40 kilometers per hour slower than the speed of a car

hence the speed of the bus is = 120-40 = 80 kilometers per hour

Required

The distance traveled

we are told that they spent the same amount of time.

let the distance covered by the bus be x  kilometers

so the distance covered by the car = (20+x)   kilometers

Step two:

from

v=d/t

time= d/v

time taken by the car

= 20+x/1201

time taken by the bus

= x/802

equate both equations

20+x/120=x/80

cross multiply

120x=80(20+x)

120x=1600+80x

120x-80x=1600

40x=1600

divide both sides by 40

x=40 kilometers

The bus travels 40 kilometers

The car travels 20+40= 60km

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)