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
Artyom0805 [142]
2 years ago
10

8. The speed of the current in a river is 6 mph. A ferry operator who works that part of the river is looking to buy a new boat

for his business. Every day, his route takes him 22.5 miles against the current and back to his dock, and he needs to make this trip in a total of 9 hours. He has a boat in mind, but he can only test it on a lake where there is no current. How fast must the boat go on the lake in order for it to serve the ferry operator’s needs? *
Mathematics
2 answers:
iren2701 [21]2 years ago
7 0

Answer:

x=9

Step-by-step explanation:

Natali [406]2 years ago
3 0
Answer: the speed of the boat on the lake is 9 mph
Step-by-step explanation:
Let x represent the speed of the boat on the lake or in still water.
The speed of the current in a river is 6 mph. This means that if the boat goes upstream against the speed of the current, its total speed would be (x - 6)mph. If the boat goes downstream against the speed of the current, its total speed would be (x + 6)mph.
Time = distance/ speed
Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. This means that the time taken to travel upstream is
22.5/(x - 6). The time taken to travel downstream is
22.5/(x + 6)
Since the total time is 9 hours, it means that
22.5/(x - 6) = 22.5/(x + 6)
Cross multiplying, it becomes
22.5(x + 6) + 22.5(x - 6) = 9
Multiplying through by (x + 6)(x - 6), it becomes
22.5(x - 6) + 22.5(x + 6) = 9[(x + 6)(x - 6)]
22.5x - 135 + 22.5x + 135 = 9(x² - 6x + 6x - 36)
22.5x + 22.5x = 9x² - 324
9x² - 45x - 324 = 0
Dividing through by 9, it becomes
x² - 5x - 36 = 0
x² + 4x - 9x - 36 = 0
x(x + 4) - 9(x + 4) = 0
x - 9 = 0 or x + 4 = 0
x = 9 or x = - 4
Since the speed cannot be negative, then x = 9
You might be interested in
What value of x makes 2x-1=-7 true?
forsale [732]

Answer:x=-3

Step-by-step explanation:

2x-1=-7

Add 1 to each side

2x=-6

Divide each side by 2

x=-3

7 0
3 years ago
Whats the fraction 18/24 reduced to its lowest items?
asambeis [7]
Hello!

\sf Answer:

The fraction 18/24, reduced to its lowest terms, is: \boxed{3/4}
_____________________________

Divide both the numerator and the denominator by the GCD of 18 and 24, which is 6:

18 ÷ 6 = 3

24 ÷ 6 = 4

It's simplest form would be 3/4. This cannot be reduced further.
3 0
3 years ago
Lydia bought a shirt at 20% off its retail price of $40. She paid a 5% tax on the price after the discount. How much did Lydia p
Alecsey [184]
40 x .80 = 32 x 1.05 = 33.60 is what she paid
3 0
3 years ago
there is a box in your attic with 3 books 4 dolls and 16 candles what is the ratio of candles to books
Kipish [7]

Answer:

the answer would be 16 to 3 which can also be shown as 16:3

Step-by-step explanation:

this is because it is asking for candles first so you put 16 next they ask for books so that is why you put 3 next

5 0
3 years ago
Use the grouping method to factor x^3 + x^2 + 5x + 5
Anuta_ua [19.1K]

Answer:

(x + 1) (x^2 + 5)

Step-by-step explanation:

Simplify the following:

x^3 + x^2 + 5 x + 5

Factor terms by grouping. x^3 + x^2 + 5 x + 5 = (x^3 + x^2) + (5 x + 5) = x^2 (x + 1) + 5 (x + 1):

x^2 (x + 1) + 5 (x + 1)

Factor x + 1 from x^2 (x + 1) + 5 (x + 1):

Answer:  (x + 1) (x^2 + 5)

4 0
3 years ago
Read 2 more answers
Other questions:
  • Correct answer gets brainliest or who ever answered first
    5·2 answers
  • What are one of the multiples of 4.<br><br>A.1,2,4,12<br>B. 9,0,3,5<br>C.ahshhansbdhs​
    14·1 answer
  • 1. A package contains 7 red candies, 4 blue candies, and 3 green candies. Three candies are drawn
    12·1 answer
  • The number of men and women receiving bachelor's degrees each year has been steadily increasing. For the years 1970 through the
    7·1 answer
  • What is the rational number that is equivalent to a -24 / -6
    13·1 answer
  • If one earthquake has a magnitude of 5 on the Richter scale and a second earthquake has a magnitude of 6,
    15·1 answer
  • Tom started an entertainment company. The net value of the company (in thousands of dollars) ttt months after its creation is mo
    15·1 answer
  • (2x + 3) + (4x + 5)<br> please help im really confused
    15·1 answer
  • Showing ALL calculations, whether this statement is valid
    15·1 answer
  • In a game, if you roll a 6 on a 6-sided number cube, you lose a turn. (a) What is the probability that you roll a 6? Explain you
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!