Answer:
2 hours, 150 miles
Step-by-step explanation:
The relation between time, speed, and distance can be used to solve this problem. It can work well to consider just the distance between the drivers, and the speed at which that is changing.
<h3>Separation distance</h3>
Jason got a head start of 20 miles, so that is the initial separation between the two drivers.
<h3>Closure speed</h3>
Jason is driving 10 mph faster than Britton, so is closing the initial separation gap at that rate.
<h3>Closure time</h3>
The relevant relation is ...
time = distance/speed
Then the time it takes to reduce the separation distance to zero is ...
closure time = separation distance / closure speed = 20 mi / (10 mi/h)
closure time = 2 h
Britton will catch up to Jason after 2 hours. In that time, Britton will have driven (2 h)(75 mi/h) = 150 miles.
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<em>Additional comment</em>
The attached graph shows the distance driven as a function of time from when Britton started. The distances will be equal after 2 hours, meaning the drivers are in the same place, 150 miles from their starting spot.
Let's solve this problem step-by-step.
STEP-BY-STEP SOLUTION:
Let's first write down the equation we are going to solve.
( 1 / 3 )h - 4 [ ( 2 / 3 )h - 3 ] = ( 2 / 3 )h - 6
To begin with, we will expand the brackets => [ ]
( 1 / 3 )h - ( 8 / 3 )h + 12 = ( 2 / 3 )h - 6
Next we will collect like terms by placing all the individual numbers on the right-side of the equation and the terms with ( h ) on the left-hand side of the equation so that we can begin making ( h ) the subject.
( 1 / 3 )h - ( 8 / 3 )h - ( 2 / 3 )h = - 6 - 12
Then we will simplify both the left-hand side and right-hand side of the equation to solve it for ( h ).
( - 9 / 3 )h = - 18
- 3h = - 18
h = - 18 / - 3
h = 18 / 3
h = 6
FINAL ANSWER:
Therefore, the answer is:
h = 6
Hope this helps! :)
Have a lovely day! <3
Answer:
A=W, B=X, C=Y, D=Z, AB=WX, BC=XY, CD=YZ, AD=WZ
(The second answer down)
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
(2x-8+2x+10)/2 = 25
(4x+2) = 2×25
4x+2 = 50
4x = 50-2
4x = 48
x = 48/4
x = 12
Solve for x:
2 (6 - x) = x (x + 5)
Expand out terms of the left hand side:
12 - 2 x = x (x + 5)
Expand out terms of the right hand side:
12 - 2 x = x^2 + 5 x
Subtract x^2 + 5 x from both sides:
-x^2 - 7 x + 12 = 0
Multiply both sides by -1:
x^2 + 7 x - 12 = 0
x = (-7 ± sqrt(7^2 - 4 (-12)))/2 = (-7 ± sqrt(49 + 48))/2 = (-7 ± sqrt(97))/2:
Answer: x = (-7 + sqrt(97))/2 or x = (-7 - sqrt(97))/2
