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
jeka57 [31]
3 years ago
13

A glassblower can produce a set of simple glasses in about 2 h. When the glassblower works with an apprentice, the job takes abo

ut 1.5 h. How long would it take the apprentice to make a set of glasses when working alone?
Mathematics
1 answer:
Snowcat [4.5K]3 years ago
7 0

Answer:

6 hours.

Step-by-step explanation:

Let t represent the time taken by apprentice in hours to make a set of glasses when working alone.  

Part of work completed by apprentice in one hour would be \frac{1}{t}.

We have been given that a glassblower can produce a set of simple glasses in about 2 hours. So part of work completed by glassblower in one hour would be \frac{1}{2}.

While working together, the job takes about 1.5 hours. So part of work completed by both in one hour would be \frac{1}{1.5}.

Now we will equate sum of work competed by both in hour by work completed by both working together is one hour as:

\frac{1}{t}+\frac{1}{2}=\frac{1}{1.5}

\frac{1}{t}\cdot 3t+\frac{1}{2}\cdot 3t=\frac{1}{1.5}\cdot 3t

3+\frac{3}{2}\cdot t=\frac{3t}{1.5}

3+1.5\cdot t=2t

3+1.5t-1.5t=2t-1.5t

3=0.5t

\frac{3}{0.5}=\frac{0.5t}{0.5}

6=t

Therefore, it will take 6 hours for the apprentice to make a set of glasses when working alone.

You might be interested in
The width of a rectangle measures (3s+t) centimeters,and it’s length measures (3s-9t) centimeters. Which expression represents t
andreyandreev [35.5K]

Answer:

12s - 16t

Step-by-step explanation:

2(3s + t) + 2(3s - 9t)

6s + 2t + 6s - 18t

12s + 2t - 18t

12s - 16t

3 0
3 years ago
A cone of radius 10 cm and height 16 cm is divided into two parts by a plane through the midpoint of its
bazaltina [42]

Answer:

The ratio of their volumes (the top to bottom half) is 1/7

Step-by-step explanation:

The given parameters are;

The radius, r, of the cone = 10 cm

The height of the cone = 16 cm

The point at which the cone is divided = The midpoint of the its axis and parallel to its base

The ratio of the of the volume of the two parts is given as follows;

The volume, V of the entire cone = 1/3 × Base area (π·r²) × Height, h

Therefore;

V = 1/3 × π × 10² × 16 =1600·π/3 =  1675.52 cm³

The height at which the cone is divided = 16/2 = 8 cm

The height, h₁ of the uppermost divided cone = 8 cm

The ratio of the radius to the height of the cone = 10/16 = 5/8

The radius r₁, of the uppermost divided cone = The height of the uppermost divided cone × The ratio of the radius to the height of the cone

∴ r₁ = 8 × 5/8 = 5 cm

The volume, V₁, of the uppermost divided cone = 1/3 × (π·r₁²) × h₁

∴ V₁ = 1/3 × π × 5² × 8 = 200·π/3 = 209.44 cm³

Which gives;

The volume of the lower cone, V₂ =  V - V₁

V₂ =  1675.52 cm³ - 209.44 cm³ = 1400·π/3 = 1466.1 cm³

The ratio of their volumes V₁ : V₂ = V₁/V₂ = (200·π/3)/(1400·π/3) = 209.44/1466.1 = 1/7.

7 0
3 years ago
Who got forza horizon 3 on xbox one
kotegsom [21]
No not meeeeeeeeeeeeee
8 0
3 years ago
Read 2 more answers
Find two numbers between 3.456 and 3.457
kow [346]

Answer:

3.4567

3.4568

Step-by-step explanation:

We need to find a number between 3.456 and 3.457. In order to do so, we need to dive deeper into the decimal to get numbers in-between.

We need to dive to the ten-thousandths place to get numbers between the two.

6 0
3 years ago
How many different committees of 4 people can be chosen from a group of 21?
sdas [7]

Answer:

There are 21 ways to choose the first person, 20 ways to choose the second, 19 ways for the third and 18 ways for the fourth so the answer is 21 * 20 * 19 * 18 = 143640.

4 0
3 years ago
Other questions:
  • The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the
    11·1 answer
  • the lateral area of a cone is 574 pi cm2. The radius is 19.6 cm. What is the slant height to the nearest tenth of a centimeter?
    7·2 answers
  • If you toss a fair coin five times and get tails every time, then the sixth toss MUST be heads. Is this true?
    7·1 answer
  • (-3) with a power of four is?
    12·1 answer
  • according to a recent survey, in 2000, 64% of households had one or more pets.Throughout the next decade, this decreased by appr
    15·1 answer
  • Jelly makes $9 per hour. she had worked 8 hours so far this week. How much has she made so far this week? Write an algebraic exp
    8·1 answer
  • Rafael's salary last year was $49,500 and he took home
    14·1 answer
  • Carlita planted 4 flowers in 6 minutes. About how many flowers can Carlita plant in 36 minutes?
    13·2 answers
  • ㅤpoint c and point d are plotted on the graph. plot points a and b to form rectangle abdc with an area of 36 square units. plot
    13·2 answers
  • During an election year, why would a senator want to determine a mode?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!