Distance = speed * time
d = st
The sports car travels d distance for t time at speed, s, 95 mph until it overtakes the family
car.
The equation for the sports car is
d = 95t
The family car travels the same distance, d, but since it left 4.5 hours earlier than the sports car, it travels for t + 4.5 time until it is overtaken. It travels at speed, 35 mph.
The equation for the family car is
d = 35(t + 4.5)
We solve the two equations as a system of equations.
d = 95t
d = 35(t + 4.5)
Since d = d, set the right sides of the equations above equal to each other.
95t = 35(t + 4.5)
95t = 35t + 157.5
60t = 157.5
t = 2.625
The answer is 2.625 hours, or 2 hours, 37 minutes, and 30 seconds.
Check:
In 2.625 hours, the sports car travels: 95 mph * 2.625 h = 249.375 miles
The family car traveled 2.625 hours plus the extra 4.5 hours, or 7.125 hours.
In 7.125 hours, the family car travels 35 mph * 7.125 h = 249.375 miles.
The cars have traveled the same distance 2.625 hours after the sports car left, so our answer is correct.
We can set up an equation to solve this problem, but first we need to write out what we know.
$20 overall
$0.24 every minute
$13.52 remaining on the card
Now that we know our information, we can set it up in an equation.
20 - 0.24x = 13.52
The 20 represents $20 overall when she first got the phone card.
We are then subtracting $20 from how must it costs a minute (which is 24 cents). The 'x' indicates the number we are trying to find (how many minutes her call lasted). Lastly, 13.52 is the result of everything, since she has $13.52 remaining on the card.
We can now solve the equation:
20 - 0.24x = 13.52
-0.24x = 13.52 - 20 /// subtract 20 from each side
-0.24x = -6.48 /// simplify
x = 27 /// divide each side by -0.24
Our solution is: x = 27.
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An easier way to solve this problem would be to first, subtract the total amount of money she had on the card when she first got it, and then the remaining total she ended up with.
$20 - $13.52 = $6.48
So, she spent a total of $6.48 on long distance calls, but since we are looking for how many minutes, we need to divide the total she spent and how much it costs per minute.
6.48 ÷ 24 = 27
We receive the same amount of minutes spent just like we did the last way we solved.
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Salma spent 27 minutes on the phone.
Answer:
negative slope
Step-by-step explanation:
using the slope equation you can see that the slope is -53
Answer:
Yes. Her solution is correct.
Step-by-step explanation:
Let's check if Jenna solution is correct:
To solve the equation 2x^2 +5x - 42 = 0, we can use Bhaskara's formula:
D = b^2 - 4ac = 25 + 4*2*42 = 25+336 = 361
sqrt(D) = 19
x1 = (-5 + 19)/4 = 14/4 = 7/2
x2 = (-5 - 19)/4 = -24/4 = -6
We must agree with Jenna's solution, because the values she found as solution are correct: with we replace these values of x in the equation, we will find 0 = 0, which is correct and proves that these values are the solution of the equation.
Three and seventy five hundredths............Hope I Helped! PS: I am a Middle Schooler and I know this!
