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
Kazeer [188]
3 years ago
6

A riverboat travels 54 km downstream in 2 hours. It travels 57 km upstream in 3 hours. Find the speed of the boat and the speed

of the stream
Mathematics
1 answer:
irakobra [83]3 years ago
5 0

Here we must write and solve a system of equations to find the speed of the boat and the speed of the stream. We will find that the boat's speed is 23km/h and the river's speed is 4km/h.

First, remember the relation:

Distance = Speed*Time.

Now let's define the variables we will be using:

  • B = boat's speed
  • R = river's speed.

When the boat travels downstream, the total speed of the boat is the speed of the boat plus the speed of the river, and we know that in that case it travels 54km in 2 hours, then:

54km = (B + R)*2h

When the boat travels upstream, we must subtract the speed of the river. In that case, we know that the boat travels 57km in 3 hours, then we have:

57km = (B - R)*3h

Then our system of equations is:

54km = (B + R)*2h

57km = (B - R)*3h

To solve this, first, we need to isolate one of the variables in one of the equations, let's isolate B in the second one:

57km = (B - R)*3h

57km/3h + R = B

19 km/h + R = B

Now we can replace that in the other equation:

54km = (B + R)*2h

54km/2h = B + R

27 km/h = B + R = (19 km/h + R) + R

Now we can solve this for R:

27 km/h = 19km/h + 2*R

27 km/h - 19km/h = 2*R

8 km/h = 2*R

(8km/h)/2 = 4km/h = R

Now that we know the value of R, we can use:

B = 19 km/h + R  = 19 km/h + 4km/h = 23 km/h

So the boat's speed is 23km/h and the river's speed is 4km/h.

If you want to learn more, you can read:

brainly.com/question/12895249

You might be interested in
What is 138 rounded to the nearest hundredth
serg [7]

Answer:

hundred and hundredth are way different 11.75 I think it would be tho

Step-by-step explanation:

4 0
3 years ago
Which statement compares the two numbers correctly?
Alex_Xolod [135]
Six hundred seventy-two thousandths <0.8
7 0
2 years ago
Read 2 more answers
A data set whose original x values ranged from 120 through 351 was used to generate a regression equation of ŷ=0.06x + 14.2. Use
lawyer [7]

Answer:

35.32

Step-by-step explanation:

The regression equation usually demonstrated as

y=a+bx.

In the above equation y is the dependent variable, x is the independent variable, a is the intercept of regression line and b is the slope of regression line.

The given regression equation is

y^=0.06x+14.2

The predicted value of y can be computed by simply putting the value of x in above equation.

So,

y^=0.06(352)+14.2

y^=21.12+14.2

y^=35.32

Thus, the predicted value of y for x=352 is 35.32.

6 0
3 years ago
Help solve this please
alukav5142 [94]

Answer:

Step-by-step explanation:

you add the balance then you will get the balance for u answer and if i didn't help u i'm sorry

4 0
3 years ago
Solve for x. −3/4(x+2)=6
Sergio039 [100]
X= -10        I hoped this helped you answer your question!
3 0
3 years ago
Other questions:
  • Judy pays $29 for 8 gallons of gas and 2 bottles of water.carmen pays $45 for 12 gallons of gas and 4 bottles of water. How much
    8·1 answer
  • NEED DONE NOW!!!!!!
    8·2 answers
  • Graph of the solution set of x+2y&gt;4
    9·1 answer
  • Which sequence of transformations creates triangles that are similar instead of congruent?
    15·2 answers
  • I need help with these questions​
    9·2 answers
  • Give me 10 cash amounts that total up to 16,100.00.
    6·1 answer
  • What is an equation in standard form of the line that has x-intercept 1 and y-intercept 4?
    12·1 answer
  • Translate this sentence into an equation.
    13·1 answer
  • Find the inverse of f(x) = -3 -4/5x
    15·1 answer
  • A cylinder has a base diameter of 12ft and a height of 12ft. What is its volume in cubic ft, to the nearest tenths place?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!