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
Brianna's chocolate chip cookie recipe will make about 3 dozen chocolate chip cookies the recipe calls for 2 1/4 cups of flour a
coldgirl [10]
Write and solve an equation of ratios to answer this.

2.25 cup              x
-------------- = -------------
0.375 cup          1 cup
                                                                                  2.25
cross-multiplying, 2.25 = 0.375x.  Solving for x, x = ---------- = 6
                                                                                   0.375

Brianna would need to use 6 cups of flour if she wants the mixture to contain 1 cup of baking soda.

6 0
3 years ago
Read 2 more answers
Find the ratio of the area inside the square but outside the circle to the area of the square
alexandr402 [8]
Area of the square:  A s = s².
Area of the circle: A c = ( 1/2 s )² π = 1/4 s² · 3.14 = 0.785 s²
Area inside the square but outside the circle: s² - 0.785 s² = 0.215 s²
The ratio:
0.215 s² : s² = 0.215 : 1 = 215 : 1000 = 43 : 200 .
4 0
3 years ago
Read 2 more answers
A telephone company charges a fixed monthly rate plus a rate per minute of usage. The company charges $155 for 100 minutes of us
torisob [31]

Answer:

The answer is D.

Step-by-step explanation:

As said in the problem, we are labeling the total minutes used <em>x </em>and the total monthly income as <em>y</em>. This means that in the graph we will be making the y-axis should represent the total monthly charges, and the x-axis should represent the total minutes.

Thus the graph should go through points (100,155) and (200,245) and its slope is:

\frac{245-155}{200-100} =0.9.

8 0
3 years ago
Read 2 more answers
What does a standard deviation of 0 indicates ?
DIA [1.3K]

What does a standard deviation of 0 indicates 0.

4 0
2 years ago
Write an equation of the line that passes through (4,-1) and is parallel to the line -3x +y= 7
Gala2k [10]

Answer:

y = 3x -13

Step-by-step explanation:

y = 3x + 7

-1 = 3(4) + b

-1 = 12 + b

-13 = b

y = 3x -13

4 0
2 years ago
Other questions:
  • jeff lives 12 miles east of stan jeff lives 16 miles north of wei what is the shortest distance stan and wei can live from eacho
    13·1 answer
  • 0.49 + 7.50 what is this answer
    11·2 answers
  • A grain silo is composed of a cylinder and a hemisphere.
    9·2 answers
  • Find up to isomorphism all abelian groups of order 48 72 84 g
    15·1 answer
  • You have 13 different books at home that you can read. You want to pick 2 to read and you don't care about what order you read t
    12·1 answer
  • If a perimeter is 20/21 what is the side length of the square
    15·2 answers
  • The diameter of a circle is 3 ft. Find the circumference to the nearest tenth.
    7·2 answers
  • Which negative angle is equivalent to a 65° angle?
    14·2 answers
  • Sum of the angles of a triangle is equal t.....? <br><br>​
    13·2 answers
  • A truck driver is driving from Nome, Alaska to Death Valley, California. Because he is traveling between locations with extreme
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!