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
Alexxx [7]
3 years ago
13

Dennis went cross country skiing for 6 hours on Saturday. He skied 20 miles uphill and then 20 miles downhill, returning to his

starting point. His uphill speed was 5 mph slower than his downhill speed. What was dennis's speed going uphill and his speed going downhill?
Mathematics
1 answer:
yulyashka [42]3 years ago
3 0

Answer: Downhill:10mph   Uphill:5mph

Step-by-step explanation:  

We are looking for Dennis’s downhill speed.

Let  

r=

 Dennis’s downhill speed.

His uphill speed is  

5

miles per hour slower.

Let  

r−5=

Dennis’s uphill speed.

Enter the rates into the chart. The distance is the same in both directions,  

20

miles.

Since  

D=rt

, we solve for  

t

and get  

t=

D

r

.

We divide the distance by the rate in each row and place the expression in the time column.

Rate

×

Time

=

Distance

Downhill

r

20

r

20

Uphill

r−5

20

r−5

20

 

Write a word sentence about the time.

The total time traveled was  

6

hours.

Translate the sentence to get the equation.

20

r

+

20

r−5

=6

Solve.

20(r−5)+20(r)

40r−100

0

0

0

=

=

=

=

=

6(r)(r−5)

6

r

2

−30r

6

r

2

−70r+100

2(3

r

2

−35r+50)

2(3r−5)(r−10)

Use the Zero Product Property.

(r−10)=0

r=10

(3r−5)=0

r=

5

3

The solution  

5

3

is unreasonable because  

5

3

−5=−

10

3

and his uphill speed cannot be negative. So, Dennis's downhill speed is  

10

mph and his uphill speed is  

10−5=5

mph.

Check. Is  

10

mph a reasonable speed for biking downhill? Yes.

Downhill:

10 mph

5 mph⋅

20 miles

5 mph

=20 miles

Uphill:

10−5=5 mph

(10−5) mph⋅

20 miles

10−5 mph

=20 miles

The total time traveled was  

6

hours.

Dennis’ downhill speed was  

10

mph and his uphill speed was  

5

mph.

You might be interested in
How to find matrics M
makkiz [27]

\left[\begin{array}{ccc}9&7\\-4&2\end{array}\right] -4M=\left[\begin{array}{ccc}-3&3\\4&-18\end{array}\right]\qquad(*) \\\\M=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]\to4M=\left[\begin{array}{ccc}4a&4b\\4c&4d\end{array}\right]

(*)\qquad\left[\begin{array}{ccc}9&7\\-4&2\end{array}\right] -\left[\begin{array}{ccc}4a&4b\\4c&4d\end{array}\right]=\left[\begin{array}{ccc}-3&3\\4&-18\end{array}\right]\\\\\left[\begin{array}{ccc}9-4a&7-4b\\-4-4c&2-4d\end{array}\right]=\left[\begin{array}{ccc}-3&3\\4&-18\end{array}\right]\\.\qquad\qquad\qquad\qquad\ \ \ \Downarrow\\(_{11})\qquad9-4a=-3\ \ \ |-9\\-4a=-12\ \ \ \ |:(-4)\\a=3\\\\(_{12})\qquad7-4b=3\ \ \ \ |-7\\-4b=-4\ \ \ \ |:(-4)\\b=1

(_{21})\qquad-4-4c=4\ \ \ \ |+4\\-4c=8\ \ \ \ |:(-4)\\c=-2\\\\(_{22})\qquad2-4d=-18\ \ \ \ |-2\\-4d=-20\ \ \ \ \ |:(-4)\\d=5\\\\Answer:\ A.\ M=\left[\begin{array}{ccc}3&1\\-2&5\end{array}\right]

3 0
3 years ago
I’m confused please help
Maru [420]
<h2>Hello!</h2>

The answer is:

Sin(A)=0.93

<h2>Why?</h2>

To solve the problem, remember to set your calculator in "degree mode"

So, we are given that the angle A is equal to 68°

So, we have that:

Sin(A)=Sin(68\°)=0.93

Hence, we have that:

Sin(A)=0.93

Have a nice day!

4 0
3 years ago
M is directly proportional to r2 <br> When r=2, m=14<br> Work out the value of m when r=12
Genrish500 [490]

we have M is durectly porpotional to r^2

so M=(k)r^2

and when r=2, m=14

so 14=(k)(2)^2

k=14/4 =7/2

so when r=12

m= (7/2)(12)^2 =(7/2)(144) = 504

8 0
3 years ago
What is the value of (-5)(-8)<br> A 40 <br> B 45 <br> C -40<br> D 13
mariarad [96]

Answer: 40

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
A solid has faces that consist of 1 pentagon, 5 congruent equilateral triangles, and 5 congruent squares. The solid has 11 verti
mrs_skeptik [129]
So the solid consist of 1 pentagon, 5 congruent equilateral triangle and 5 congruent squares and has 11 vertices so the number of edges of this solid is 20. I hope you are satisfied with my answer and feel free to ask form more if you have more clarifications.
5 0
3 years ago
Other questions:
  • Which expression means 2 less than a number? p + 2 p – 2 2 × p 2 ÷ p
    14·2 answers
  • What Is 1,270 rounded to the nearest hundred?
    12·1 answer
  • Given angle measurements of 40°, 45°, and 95°, how many triangles can be constructed?
    12·2 answers
  • Write a two column proof. given: bd perpindicular to ac and bd bisects ac prove: abd = cbd
    13·1 answer
  • Jordan makes 100 3-point shots per basketball practice. She makes 44 of these shots. What decimal represents the number of the s
    10·2 answers
  • The number of hours a group of 12 children in Mrs. Smith's kindergarten class read in a day.
    5·1 answer
  • Please help.........
    11·1 answer
  • E the location for each of the following staring points andlocation changes6. (5.3), 67- 8.5.3
    12·1 answer
  • a square has a perimeter of 38 inches. We want to know the length of each side. choose the best model for the problem
    10·2 answers
  • Subtract: 5/8 - 1/4 <br>A. 1/4 <br>B. 3/8 <br>C. 1/2 <br>D. 3/4​
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!