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
tankabanditka [31]
2 years ago
12

A boat covers 25 km upstream and 44 km downstream in t hours. Also, it covers 15 km upstream and 22 km downstream in 5 hours. Fi

nd the speed of the boat in still water and that of the stream.​
Mathematics
2 answers:
aniked [119]2 years ago
7 0

9514 1404 393

Answer:

  boat speed: (7t -95)/(6t² -110t +500)

  stream speed: (37t -345)/(6t² -110t +500)

Step-by-step explanation:

The relation between time, speed, and distance is ...

  time = distance/speed

The boat speed (b) is added to the stream speed (s) going downstream. The stream speed is subtracted going upstream. The given relations tell us ...

  25/(b-s) +44/(b+s) = t

  15/(b-s) +22/(b+s) = 5

This gives us 2 equations in 3 unknowns, so we can only provide a solution in terms of one of the unknowns. Since we are asked for the speeds, they will be provided in terms of t.

Subtracting the first equation from 2 times the second gives ...

  2(15/(b-s) +22/(b+s)) -(25/(b-s) +44/(b+s)) = 2(5) -(t)

  5/(b-s) = 10 -t

  5/(10 -t) = b -s

Substituting for b-s in the second equation gives ...

  15/(5/(10-t)) +22/(b+s) = 5

  30 -3t +22/(b+s) = 5

  22/(b+s) = 3t -25

  22/(3t -25) = b+s

Adding the equations for the sum and difference of speeds, we get ...

  (b-s) +(b+s) = 5/(10-t) +22/(3t -25)

  2b = (5(3t -25) +22(10 -t))/((10-t)(3t-25)) = (95 -7t)/((10-t)(3t-25))

  b = (7t -95)/(6t² -110t +500)

Subtracting the equations for sum and difference of speeds, we get ...

  (b+s) -(b-s) = 22/(3t -25) -5/(10 -t)

  2s = (22(10-t) -5(3t -25))/((10-t)(3t-25))

 s = (37t -345)/(6t² -110t +500)

__

The speed of the boat in still water is (7t -95)/(6t² -110t +500) km/h.

The speed of the stream is (37t -345)/(6t² -110t +500) km/h.

__

Note that these solutions only make sense for values of t between 25/3 and 345/37, approximately 8.33 < t < 9.32. For t=9 hours, the boat speed is 8 km/h and the stream speed is 3 km/h.

Liula [17]2 years ago
5 0

<h2>Speed of boat in still water</h2><h2>=8km/hr </h2><h2>Speed of stream=3km/hr</h2>

Step-by-step explanation:

Speed of boat in still water=x km/hr

Speed of stream=y km/hr Speed of upstream=x-y km/hr

Speed of downstream=x+y km/hr

Let 1/(x-y)=a and 1/(x+y)=b

Time to go 25km up and 44 down=9

25a+44b=9----->(1)

Time to go 15km up and 22km down=5

15a+22b=5------>(2)

(2) x 2=> 30a+4463D10- ->(3)

(3)-(1)=>5a=1

a=1/5

1/(x-y)=1/5

x-y=5--->(4)

Putting a=1/5 in (1),

5+44b=9

44b=4

b=1/11

1/(x+y)=1/11

x+y=11---->(5)

(4)+(5)=>2x=16

<h2>x=8</h2>

<h2>y=3</h2>
You might be interested in
1. f(x) = -x + 6x-2<br><br> Find the vertex, y-intercept and x-intercept
expeople1 [14]

Answer:y intersept =-2

X interesept=2/5

Step-by-step explanation: let y=0

0=5x-2

2=5x

X=2/5

Let x=0

Y=-2

5 0
2 years ago
Indicate true or false as to whether the following equation is quadratic 2x-4x+1=0
saul85 [17]
The answer to the problem would be false
3 0
2 years ago
Read 2 more answers
the ages of three siblings are all consecutive integers the sum of their ages is 39 how old is the youngest sibling variable equ
Verdich [7]

Answer:

Step-by-step explanation:

Let x = the age of the youngest child

Let x + 1 = the age of the middle child

Let x + 2 = the age of the oldest child

x + x + 1 + x + 2 = 39

3x + 3 = 39

3x = 36

x = 12 years

8 0
2 years ago
In a certain fraction, the numerator is 4 less than the denominator. If 4 is added to both the numerator and the denominator , t
love history [14]

Answer:

Step-by-step explanation:

If the new fraction is 8/12 I will show how to find it.

Let's say the original denominator is x, then the numerator is x-4, so we have (x-4)/x.

Then it says f we add 4 to both, so now we have x/(x+4) this equals 8/12.  Now, keep in mind -4 cannot be an answer because it would make x/(x+4) be divided by 0 which wouldn't exist.

Now we just use algebra.

x/(x+4) = 8/12

12x = 8(x+4)

12x = 8x + 32

4x = 32

x = 8

So the original fraction (x-4)/x = (8-4)/8 = 4/8

5 0
3 years ago
(10 points for the answer)<br><br> y=
Nat2105 [25]
Answer: y=1x+4
Solving Steps:
5 0
2 years ago
Other questions:
  • 5.1÷104 Need Rounded to the nearest tenth. Can't seem to figure it out.
    14·1 answer
  • Convert 1.8 decimeters to millimeters​
    7·1 answer
  • What kind of number is a negative number?
    9·1 answer
  • Which of the following is true about the graphs below?
    9·1 answer
  • A store buys 77 1 2 pounds of mulch in a large shipment. They divide the mulch up into bags that can each hold 2 1 4 pounds. The
    5·1 answer
  • What is the area of this object?
    11·1 answer
  • 12. What is the value of y that satisfies the equation: y/3 =<br> 12
    11·1 answer
  • 50 points if its correct with brainliest!! How many times smaller will a number become if you decrease it by 20%.
    10·1 answer
  • HELPPP pls quick thanks &lt;3
    9·1 answer
  • The sum of the digits of a two-digit number is 11.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!