Question

A car travels at an uniform speed. At 2 pm it is at a distance of 180 km and at 6pm it

is at 360 km. Using section formula, find at what distance it will reach 12 midnight.

Answer 1

Answer:

360

Explanation:

Lets represent the given information in the form of coordinates while taking time at x axis and distance covered on y axis.

So, our points are

A (x1, y1) = (2, 180)

B (x2, y2) = (6, 360)

C (x3, y3) = (12, y)

Now the point B divides the Point A and C in the ratio 4 : 6 or 2 : 3.

So, lets take

k1 = 2

k2 = 3

using the formula

y = (k1.y3 + k2y1)/(k1 +k2)

360 = (2y + 3x180)/ (2 + 3)

360 =  (2y + 540)/ (5)

360x5 = 2y + 540

1800 = 2y + 540

2y = 1800 - 540

2y = 1260

y = 630 km

So, he will be at a distance of 360 km at 12am midnight