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
Pachacha [2.7K]
3 years ago
8

Pilar is playing with a motorized toy boat. She puts the boat in a lake and it travels 400m at a constant speed. On the way back

to Pilar, the boat travels the same route at the same speed for 2 minutes, and then Pilar uses the remote control to increase the boat's speed by 10 m/min. So the return trip is 60 seconds faster. How long does the return trip take?
Mathematics
1 answer:
ankoles [38]3 years ago
3 0

Answer:

The trip normally takes 8 minutes

Step-by-step explanation:

The given information states that the away distance the boat traveled = 400 m

The time traveled at the same initial  speed , v₁, by the boat on the way back = 2 minutes

The increase in speed of the boat by Pilar =  10 m/min

The new speed, v₂ = v₁ + 10

The time for the return trip, t₂ = 60 seconds (1 minute) faster than time for the trip, t₁

t₂ = t₁ - 1

Therefore we have;

v₁ × t₁ = v₁×2 + v₂×(t₂-2) = 400

v₁×2 + (v₁ + 10)×(t₂-2) = 400

(v₁ + 10)×t₂ - 20 = 400

But v₁ = 400/t₁ = 400/(t₂ + 1)

Which gives;

(400/(t₂ + 1) + 10)×t₂ - 20 = 400

10×(t₂²+ 36·t₂-2)/(t₂+1) = 400

10·t₂²+ 10·t₂-420 = 0

t₂²+ t₂-42 = 0

(t₂ - 7)(t₂ + 6) = 0

t₂ = 7 minutes or -6 minutes

Given that t₂ is a natural number, we have, t₂ = 7 minutes

Whereby, t₂ = t₁ - 1, we have;

7 =  t₁ - 1

t₁ = 1 + 7 = 8 Minutes

The trip normally takes 8 minutes

You might be interested in
A research organization keeps track of what citizens think is the most important problem facing the country today. They randomly
Nuetrik [128]

Answer:

Step-by-step explanation:

From the information given, the population is divided into sub groups. Each group would consist of citizens picking a particular choice as the most important problem facing the country. The choices are the different categories. In this case, the null hypothesis would state that the distribution of proportions for all categories is the same in each population. The alternative hypothesis would state that the distributions is different. Therefore, the correct test to use to determine if the distribution of​ "problem facing this country ​today" is different between the two different​ years is

A) Use a​ chi-square test of homogeneity.

8 0
3 years ago
Any help would be great
xz_007 [3.2K]

Answer:

329 degrees F

Step-by-step explanation:

If you plug in your known variables into the calculator, you would get the answer 329 for <em>F</em>. You plug in 165 as <em>C </em>in the equation to find your answer.

5 0
3 years ago
A line has an equation of y = - 3x + 8. What is the y-intercept of the line? Please enter your answer as a coordinate (x, y). *
mina [271]

Answer:

(0, 8).

Step-by-step explanation:

The y intercept occurs when  = 0, so we have the equation:

y = -3(0) + 8

y = 0 + 8

y = 8.

The answer is (0, 8).

6 0
3 years ago
A box of the Tic Tacs contains 44 of the 1 1/2- calorie flavored breath mints. How many calories are there in a box of Tic Tacs?
masya89 [10]

Answer:

66

forty-four times 1.5 equals 66

6 0
2 years ago
Figure A is a scale image of Figure B, as shown.
Inessa [10]

9514 1404 393

Answer:

  x = 2

Step-by-step explanation:

Using the scale factor, we have ...

  x/8 = 0.25/1

  x = 8(0.25) . . . . multiply by 8

  x = 2

_____

<em>Additional comment</em>

I like to write proportions with the variable in the numerator. That way they are easily solved by a single multiplication. The trick is to get corresponding parts in the same positions. Here, the fractions are written ...

  B/A = smaller part / larger part = x/8 = 0.25/1

5 0
3 years ago
Other questions:
  • (Please help!!!!!) Ren finds 6 peanuts, 4 raisins, 3 cranberries, and 5 chocolate chips in a handful of trail mix.For every 9 pi
    14·2 answers
  • Which sequence are geometric? Check all that apply
    11·1 answer
  • Solve the equation 9x + 3y -2x
    6·1 answer
  • Suppose that a new fuel-efficient European car travels an average of 26 kilometers on 1 liter of gas. If gas costs 2.25 euros pe
    9·2 answers
  • Point slope form for (-10,3) and (-2,-5)
    14·2 answers
  • If the sum of interior angle measures of a polygon is 720º, how many sides
    14·1 answer
  • How many points need to be removed from this graph
    12·2 answers
  • The perimeter of a rectangle is 30 cm. The height is 5 cm . what is the area of that rectangle.​
    6·2 answers
  • Question:
    10·1 answer
  • Please answer my question, this is the third time i've asked. (75 Points)
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!