Question

Two cars start from the same point on the flat ground. The first can drives off directly north at 25ms^1. Two seconds later the second car drives off directly East at 20ms^-1. After how many seconds are they 1 km apart?​

Answer 1

Answer:

Step-by-step explanation:

Two cars start out at the same point.

One car starts out driving north at 25 mph.

Two hours later the second car starts driving east at 20 mph.

How long after the first car starts traveling does it take the two cars to be 300 miles apart?

:

This is pythag problem; a^2 + b^2 = c^2

:

Let t = driving time of 1st car

then

25t = distance driven by the 1st car (a)

:

Let (t-2) = driving time of 2nd car

then

20(t-2) = distance driven by the 2nd car

Simplify to:

(20t-40) (b)

:

c = 300 mi

:

(25t)^2 + (20t-40)^2 = 300^2

FOIL

625t^2 + (400t^2 - 1600t + 1600) = 90000

:

625t^2 + 400t^2 - 1600t + 1600 - 90000 = 0

:

1025t^2 - 1600t - 88400 = 0

:

Simplify, divide by 25

41t^2 - 64t - 3536 = 0

:

Solve this equation using the quadratic formula; a=41; b=-64; c=-3536

:

The positive solution: x ~ 10.1 hrs after the 1st car departs