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
Viktor [21]
3 years ago
6

Adam started to run at a rate of 6 mph from city A towards city B, which is 18 miles away. Ten minutes later, Benjamin started t

o run from city B towards city Aand simultaneously, Caroline started to bicycle at a rate of 11 mph from city A towards city B. If Caroline caught up to Benjamin 50 minutes after passing Adam, what was Benjamin's rate in mph?
Mathematics
1 answer:
amm18123 years ago
5 0

Answer:

<u>Benjamin's rate in mph was 6.44</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

  • Rate or speed of Adam = 6 mph
  • Ten minutes later, Benjamin started to run from city B towards city A
  • Simultaneously, Caroline started to bicycle at a rate of 11 mph from city A towards city B

2. If Caroline caught up to Benjamin 50 minutes after passing Adam, what was Benjamin's rate in mph?

A. Let's calculate when Caroline caught up Adam:

Adam's rate = 6 mph

Caroline's rate = 11 mph

10 minutes = 1/6 of an hour

Distance covered by Adam when Caroline started to bike = 6 * 1/6 = 1 mile

t = Time it took Caroline to catch up to Adam

Therefore, we can solve for t, this way:

11t = 6t + 1

11t - 6t = 1

5t = 1

t = 1/5 of an hour

t = 12 minutes

Caroline passed Adam after biking 12 minutes, therefore she caught up to Benjamin 50 minutes later, or after 62 minutes.

B. Let's calculate the distance she covered after 62 minutes, this way:

62 minutes = 1 hour and 2 minutes or 1 2/60 or 1.03

Distance covered by Caroline = Time * rate

Replacing with the values we have:

Distance covered by Caroline = 1 2/60 * 11

Distance covered by Caroline = 11 11/30 or 11.37 miles

Let's recall the distance from city A to city B is 18 miles, therefore Benjamin covered 6.63 miles (18 - 11.37) when Caroline caught up to him

C. Finally let's calculate Benjamin's rate, this way:

Rate = Distance/Time

Replacing with the values we know:

Rate = 6.63/1.03

<u>Rate = 6.44 mph (rounding to the next hundredth)</u>

You might be interested in
A new actuarial test (Test A) was developed as a possible replacement for an old actuarial test (Test B). An actuary claimed tha
alisha [4.7K]
Test A is the answer
4 0
2 years ago
The slant height is 8 inches and the diameter is 8 inches, what
Lynna [10]

Answer:

150.85inches

Step-by-step explanation:

TSA of cone= πr(r+l)

= 22/7×4(4+8)

= 150.85inches

4 0
2 years ago
A and B are two similar ornaments in the shape of a fish. The surface area of 44.8 cm and the surface area of B 179.2 cm Find th
ASHA 777 [7]

Answer:

400 cm

Step-by-step explanation:

1 cm = 1000m

44.8 cm=?

8 0
2 years ago
PLEASE FINISH QUICKLYYY!!!!!!
swat32

1) Area = leg(1) * leg(2) * .5 = 15 * 36 * .5 = 270

Perimeter = leg(1) + leg(2) + hypotenuse = 15 + 36 + 39 = 90

2) Area = leg(1) * leg(2) = 20 * 80 = 1600

3) Median (divides it in 1/2)

4) Both (divides it in 1/2 and makes a 90 degree angle w/ base)

5) Altitude (makes 90 degree angle w/ base)

6)sqrt(30^2 + 16^2) = sqrt( 900 + 256) = sqrt(1156) = 34

7) sqrt(24^2 + 18^2) = sqrt( 576 + 324) = sqrt(900) = 30

8) sqrt(40^2 + 96^2) = sqrt(1600 + 9216) = sqrt(10816) = 104

9) sqrt(150^2 - 90^2) = sqrt(22500 - 8100) = sqrt(14400) = 120

10) sqrt(35^2 - 25^2) = sqrt(1225 - 625) = sqrt(600) = 10sqrt(6), approx. 24.5

7 0
3 years ago
In a set of 25 aluminum castings, four castings are defective (D), and the remaining twenty-one are good (G). A quality control
lianna [129]

Answer:

The sample space for selecting the group to test contains <u>2,300</u> elementary events.

Step-by-step explanation:

There are a total of <em>N</em> = 25 aluminum castings.

Of these 25 aluminum castings, <em>n</em>₁ = 4 castings are defective (D) and <em>n</em>₂ = 21 are good (G).

It is provided that a quality control inspector randomly selects three of the twenty-five castings without replacement to test.

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

{n\choose k}=\frac{n!}{k!(n-k)!}

Compute the number of samples that are possible as follows:

{25\choose 3}=\frac{25!}{3!\times (25-3)!}

      =\frac{25\times 24\times 23\times 22!}{3!\times 22!}\\\\=\frac{25\times 24\times 23}{3\times 2\times 1}\\\\=2300

The sample space for selecting the group to test contains <u>2,300</u> elementary events.

6 0
3 years ago
Other questions:
  • Round each whole number to the given place value. <br> 437 to the tens place
    9·1 answer
  • The Appalachian Trail is about 2175 miles long.If a hiker averages 12 miles each day, how long will it take her to hike the leng
    14·2 answers
  • |10 - (-43)| absoulute value
    5·2 answers
  • 1. Find the derivative of <img src="https://tex.z-dn.net/?f=f%28x%29%3D6%2Fx" id="TexFormula1" title="f(x)=6/x" alt="f(x)=6/x" a
    10·1 answer
  • Heating oil is to be poured at the constant rate of 4.5 gallons per minute into a 400-gallon tank that already contains 115 gall
    5·1 answer
  • the temperature was -6 f. it rose so that the temperature was 0 f. what represents the change in temperature
    14·1 answer
  • Find the volume of this prism 41cm2 11cm
    5·1 answer
  • Imagine that a family of three (Alice, Bill, and Chester) plays bingo at home every night. Each night, the chance that any one o
    5·2 answers
  • 5
    8·2 answers
  • Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of k, where k
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!