1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Andru [333]
2 years ago
12

A car travels 133 mi averaging a certain speed. If the car had gone 30 mph​ faster, the trip would have taken 1 hr less. Find th

e​ car's average speed.
Mathematics
1 answer:
Natali5045456 [20]2 years ago
7 0

Answer:

49.923 mph

Step-by-step explanation:

we know that the car traveled 133 miles in h hours at an average speed of x mph.

That is, xh = 133.

We can also write this in terms of hours driven: h = 133/x.

 

If x was 30 mph faster, then h would be one hour less.

That is, (x + 30)(h - 1) = 133, or h - 1 = 133/(x + 30).

We can rewrite the latter equation as h = 133/(x + 30) + 1

We can then make a system of equations using the formulas in terms of h to find x:

h = 133/x = 133/(x + 30) + 1

133/x = 133/(x + 30) + (x + 30)/(x + 30)

133/x = (133 + x + 30)/(x + 30)

133 = x*(133 + x + 30)/(x + 30)

133*(x + 30) =  x*(133 + x + 30)

133x + 3990 = 133x + x^2 + 30x

3990 = x^2 + 30x

x^2 + 30x - 3990 = 0

<em><u>Using the quadratic formula: </u></em>

x = [-b ± √(b^2 - 4ac)]/2a  

= [-30 ± √(30^2 - 4*1*(-3990))]/2(1)  

= [-30 ± √(900 + 15,960)]/2

= [-30 ± √(16,860)]/2

= [-30 ± 129.846]/2

= 99.846/2  -----------  x is miles per hour, and a negative value of x is neglected, so we'll use the positive value only)

= 49.923

Check if the answer is correct:

h = 133/49.923 = 2.664, so the car took 2.664 hours to drive 133 miles at an average speed of 49.923 mph.

If the car went 30 mph faster on average, then h = 133/(49.923 + 30) = 133/79.923 = 1.664, and 2.664 - 1 = 1.664.

Thus, we have confirmed that a car driving 133 miles at about 49.923 mph would have arrive precisely one hour earlier by going 30 mph faster

You might be interested in
GUYS AGAIN PLEASE HELP 1 MILLION POINTS, get it wrong i report you!!
Evgesh-ka [11]

Answer:

Sweats heavily , I hope the answer is FALSE

Step-by-step explanation:

Is it right. Please mark Brainliest if is.

4 0
2 years ago
Lance earned $27 for mowing 3 lawns. What is the rate earned per lawn mowed?
Sliva [168]

Answer: $9 dollars

Step-by-step explanation:

27 divided by 3 = 9

*** If you found my answer helpful please give me the brainliest :) ***

4 0
3 years ago
Read 2 more answers
What is a collinear point?
Viefleur [7K]
Three or more points on a straight line
5 0
2 years ago
Read 2 more answers
Write an equation for the line passing through the points (-5,15) and (20,25). Show how you found your answer.
olasank [31]

The point-slope form:

y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}

We have the points (-5, 15) and (20, 25). substitute:

m=\dfrac{25-15}{20-(-5)}=\dfrac{10}{25}=\dfrac{2}{5}\\\\y-15=\dfrac{2}{5}(x-(-5))\\\\y-15=\dfrac{2}{5}(x+5)\qquad|\text{use distributive property}\\\\y-15=\dfrac{2}{5}x+2\qquad|\text{add 15 from both sides}\\\\y=\dfrac{2}{5}x+17\qquad|\text{multiply both sides by 5}\\\\5y=2x+85\qquad|\text{subtract 2x from both sides}\\\\-2x+5y=85\qquad|\text{change the signs}\\\\2x-5y=-85

Answer:

point-slope form: y-15=\dfrac{2}{5}(x+5)

slope-intercept form: y=\dfrac{2}{5}x+17

standard form: 2x-5y=-85

7 0
3 years ago
WHAT IS THIS???????​
kodGreya [7K]

Answer:

i think you have to mark where the dog leashes go on the line plot based on their length?? for example, a 3 foot dog leash is on the <em>list</em>, so maybe you're supposed to put an X or something above the number 3 on the <em>line plot</em>? so sorry if this didn't help..

7 0
3 years ago
Other questions:
  • Andrea's rock collection has 25 fewer rocks than Claudia's collection. Andrea's collection contains 125 rocks. Which equation ca
    12·2 answers
  • Find the coefficient of the 'x' term when multiply: (x-7)(x+3)
    10·1 answer
  • Which of the following is a graph of f(x)=x^2+2x-3/x+2
    7·2 answers
  • After going three quarters of my journey. I found that I had covered 15 km distance. How much distance left?
    15·1 answer
  • What is the solution set to the inequality 7z+5&gt;47
    9·1 answer
  • What is the value of t in the following equation? t + 14 = 2 712
    12·1 answer
  • (-3x^2y)^2<br> (−3x <br> 2<br> y) <br> 2
    15·1 answer
  • F() = x2 + 1<br> g(x) = 5 - x<br> (f+g)(x) =
    13·1 answer
  • A sphere and a cylinder have the same radius and height. The volume of the cylinder is 27 ft.
    6·1 answer
  • 1+5÷5×3 <br>please help ​
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!