Abird leaves its nest and travels 12 miles per hour downwind for x hours. on the return trip, the bird travels 2 miles per hour slower and has 3 miles left after x hours.
what's the distance of the entire trip?
how long does the entire trip take?

a) 36 miles

b) 3.3 hours

Step-by-step explanation:

Given:

Downwind speed of the bird = 12 mph

Time for travel = x hours

Speed at the return = 12 mph - 2 mph = 10 mph

Distance left = 3 miles

Now,

The distance covered at 12 mph = 12 × x = 12x

now,

distance covered with speed 10 mph in x hours = 10x

also,

10x + 3 = 12x

or

2x = 3

or

x = 1.5 hours

Therefore,

the distance of the entire trip = 2 × 12x = 2 × 12 × 1.5 = 36 miles

Now,

the time taken to complete remaining 3 miles while returning = =0.3 hours

hence,

the total time for the entire trip = 2 × 1.5 + 0.3 = 3.3 hours

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'.

y + 11 = (1/4)(x + 16)

step-by-step explanation: