Word problem on finding speed based on time, distance

[ducmod]

Mod note: Moved the text under Relevant equations to the attempt section
1. Homework Statement
Hello!
Can't wrap my head around this easy problem. Would be grateful for help in spotting out my mistakes.
One day, Donnie observes that the wind is blowing at 6 miles per hour. An unladen swallow
nesting near Donnie's house flies three quarters of a mile down the road (in the direction of
the wind), turns around, and returns exactly 4 minutes later. What is the airspeed of the
unladen swallow? (Here, `airspeed' is the speed that the swallow can
y in still air.)

Homework Equations

The Attempt at a Solution

Here is how I approached the solution:
x - airspeed in miles/ hour
v1 - speed of the swallow in the direction of the wind, in miles/hour
v2 - speed on the way back in miles/ hour
v1 = x + 6
v2 = x - 6
time to fly 3/4 of a mile = 3/4 : v1
time to fly back = 3/4 : v2
overall time = 1/15 (4 minutes)

then, overall time: 1/15 = 3/4 : (x+6) + 3/4 : (x-6)

When I try to solve this, I do not get the result any way near the desired one, and I do not get correct roots for x.

 

[Qwertywerty]

When I try to solve this, I do not get the result any way near the desired one, and I do not get correct roots for x.

Check that calculation once again .

 

[ducmod]

Check that calculation once again .

I did quite a few times :)
the answer should be 24 miles/hour

15*3(x-6) + 15*3(x+6) - 4(x^2 - 36) = 0
-4x^2 + 90x + 144 = 0
doesn't give the 24m/h

 

[Qwertywerty]

I did quite a few times :)
the answer should be 24 miles/hour

15*3(x-6) + 15*3(x+6) - 4(x^2 - 36) = 0
-4x^2 + 90x + 144 = 0
doesn't give the 24m/h

Okay - show your working of the quadratic equation's solution . It's correct till now .

 

[ducmod]

Okay - show your working of the quadratic equation's solution . It's correct till now .

-90 +- √90*90 +4*4*144 / -16
-90 - 102 / - 16 = 12

 

[Qwertywerty]

-90 +- √90*90 +4*4*144 / -16
-90 - 102 / - 16 = 12

Two things - First - You should be using brackets appropriately .
Second - What's the formula used to solve a quadratic ? Does the denominator use 4*a or 2*a ?

 

[ducmod]

Two things - First - You should be using brackets appropriately .
Second - What's the formula used to solve a quadratic ? Does the denominator use 4*a or 2*a ?

 

[ducmod]

exactly! thank you, and sorry for not posting correct brackets. of course, it is 2a in the denominator :) Thank you!