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
alina1380 [7]
3 years ago
15

On a trip, Duke encounters some road construction that slows him down. While he is able to go 60 mph on the highway and 40 mph t

hrough cities, he can only go 20 mph past the construction. He spends one half the time on the highway as he does in construction, so the 380-mile trip takes 11 hours. How much of this time does he spend on the highway, in the city, and through road construction?
Mathematics
1 answer:
natulia [17]3 years ago
3 0

Answer:

Time taken by Duke on the highway = 3 hours

Time spent on the construction = 6 hours

Time spent in the city = 2 hours

Step-by-step explanation:

Speed by which Duke travels a distance on highway d_1 = 60 mph

Let the time taken to travel on highway = t_1 hours

Distance traveled = 60t_1 miles

Speed in the city = 40 mph

Let the time taken = t_2 hours

Distance traveled in the city = 40t_2 miles

Speed on the construction = 20 mph

Let the time spend on the construction = t_3 hours

Distance traveled on the construction = 20t_3 miles

Since, total distance covered = 380 miles

d_1+d_2+d_3=60t_1+40t_2+20t_3

He spends one half the time on the highway as he does on the construction,

t_3=2t_1

Total time spent in the trip = 11 hours

Therefore, t_1+t_2+t_3=11

t_1+t_2+2t_1=11

t_2=11-3t_1

From equation (1),

60t_1+40(11-3t_1)+20(2t_1)=380

60t_1-120t_1+40t_1+440=380

440-20t_1=380

20t_1=440-380

t_1=\frac{60}{20}

t_1=3 hours

t_2=11-3t_1=2 hours

t_3=2t_1=6 hours

Therefore, time taken by Duke on the highway = 3 hours

Time spent on the construction = 6 hours

Time spent in the city = 2 hours

You might be interested in
A quadrilateral with no sides parallel and diagonals that are perpendicular
Drupady [299]
<h3>Answer:  Quadrilateral</h3>

======================================================

Explanation:

Of your original given list, let's write down the parallelograms. They are:

  • Parallelogram
  • Rectangle
  • Rhombus
  • Square

So we cross those off the list since we want a quadrilateral with no sides parallel. A parallelogram, by definition, is a quadrilateral with both pairs of opposite sides that are parallel.

We can also rule out the trapezoids because a trapezoid is a four sided figure (quadrilateral) where we have exactly 1 pair of parallel sides, while the other sides are not parallel.

Lastly, we can rule out the kite because any kite has perpendicular diagonals.

The only thing left is quadrilateral. In my opinion this answer should be more specific and say "quadrilateral that isn't a parallelogram, a trapezoid, or a kite", but I think I see what your teacher was going for here.

5 0
3 years ago
Kaylee has 4 1/2 yards of fabric. She wants to make an outfit that requires 6 1/3 yards of fabric. How much more fabric will she
Artyom0805 [142]

Answer:

1 5/6

Step-by-step explanation:

6 1/3-4 1/2= 19/3-9/2= 38/6-27/6= 11/6= 1 5/6

Ans: She will need 1 5/6 more fabric.

6 0
3 years ago
I need help againnnn, the 2nd and 3rd pics are supposed to be together
Trava [24]

Answer:

umm what do you mean can like you explain

4 0
3 years ago
Read 2 more answers
What is the inverse of the function below?
vredina [299]

Answer:

f^-1(x) = x + 5

Step-by-step explanation:

f(x) = x-5

y = x-5

Exchange x and y

x = y-5

Solve for y

x+5 = y-5+5

x+5 =y

The inverse is x+5

4 0
3 years ago
What is a irrational number between 9.5 and 9.7
Oliga [24]

Step-by-step explanation:

x be an irrational number between 9.5 and 9.7.

So, we consider that  x = 9.562536941412578914...

Rounding to the nearest hundredth

x = 9.56.

9.56763865854637984..... (rounded 9.57)

irrational because it has no pattern

6 0
3 years ago
Read 2 more answers
Other questions:
  • John (whose line of sight is 6 ft above horizontal) is trying to estimate the height of a tall oak tree. He first measures the a
    8·1 answer
  • 6 inches for every horizontal change of 12 inches
    12·1 answer
  • How many rainbow six events has there been since beta?
    15·1 answer
  • Abi takes a job with a starting salary of $100,000 for the first year. She earns a 3% increase each year. How much does Abi make
    11·2 answers
  • A(-6)=-42<br> solve for a
    13·2 answers
  • What is 1+1? pls dont hate on me
    13·2 answers
  • What are the answers to these 4 questions
    8·1 answer
  • Lexie drives her car 96 miles using 4 gallons of gas. How many miles per gallon does her car get?
    9·2 answers
  • Find five solutions for the linear equations 2x + y =5
    12·1 answer
  • Evaluate 3x for x = -2, x = 1, and x = 3.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!