Antony and lily started moving in opposite directions from the same point at the same time. if antony was biking with average 12 mph speed and lily was walking by 4 mph, how soon the distance between them will be 76 miles?

t=4.75 hours (4 hours+45 minutes)

Step-by-step explanation:

Distance At Constant Speed

An object moving at a constant speed v during a time t will travel a distance x given by

x=vt

The velocity and displacement are vectors because they are pointed toward a certain direction. When the directions are in the same line of action, we only need to adjust the signs to tell objects moving in the same or in opposite directions.

The condition of the problem states Antony and Lily started moving in opposite directions from the same point at the same time. The moving speed of Antony is 12 mph and the speed of Lily is 4 mph. Let's call the distance covered by Antony and the distance covered by Lily, both at the same time t (in hours)

The total distance between them is  

t=4.75 hours (4 hours+45 minutes)

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.