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
Convert 0.0425 as a fraction in its simplest form​
Sholpan [36]

Answer:

17/400

Step-by-step explanation:

.0425 = 425/10,000

this can be simplified to be 17/400

8 0
3 years ago
Write the slope-intercept form of the equation of each line
lesya692 [45]

Answer:

1.) y= \frac{1}{6} x + \frac{13}{6}

2.) y = \frac{4}{5} x - 3

3.) y = 3x - 2

4.) y = \frac{13}{7} x - 8

5.) y = \frac{1}{4} x + 4

6.) y = 9x - 1

7.) y = -\frac{1}{2} x - 4

8.) y = -\frac{10}{3} x + 2

9.) y = \frac{7}{8}x - 1

10.) y = -5

4 0
3 years ago
Gravel covers 66 feet of a path. This distance represents 55% of the length of the path.
Harman [31]

Answer:

120 ft

Step-by-step explanation:

Represent the path length by P.

Then 0.55P = 66 ft, and

       66 ft

P = ---------- = 120 ft

       0.55

8 0
3 years ago
What are the x and y-intercepts of the line described by the equation? 3x−9y=10.8
zheka24 [161]

Answer:

y intercept = (0,-1.2)

x intercept = (3.6,0)

Step-by-step explanation:

For y-int, x=0

3(0)-9(y)=10.8

9y=-10.8

y= -1.2

For x-int, y =0

3x - 9(0)=10.8

3x=10.8

x=3.6

7 0
3 years ago
Help please ?!?!?!!???????!???!???!!????!!??!??!?!?!!??!?!!????
wariber [46]
No association because it’s scattered
8 0
3 years ago
Other questions:
  • Laura is planning a party for her son. She has $50 dollars remaining in her budget and wants to provide one party favor per pers
    10·1 answer
  • Eight times the difference of a number and seventeen is thirty"?
    6·2 answers
  • Which solution contains the correct number of significant digits for the product 2.80 mm · 0.1 mm.
    11·1 answer
  • How many sides does a polygon have if the sum of its interior angles is 1,260º?
    8·1 answer
  • The perimeter of a triangle is 17 inches. One side is 5 inches, and another is 4 inches. What is the length of the third side?
    10·1 answer
  • Leo invests $2,000 loses money at a rate of 4%. How much is the investment worth in total at the end of 3 years? Round to the ne
    15·1 answer
  • A fair coin is flipped 4 times. It lands facing heads up 3 out of 4 times. The probability of a fair coin landing heads up on on
    13·1 answer
  • Solve x/-4-(-8)=12<br><br> Is the Answer -80, 80, 16 or -16
    8·1 answer
  • PLEASE HELP!
    13·1 answer
  • Solve the math problem
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!