A ladder

The bottom rung of a ladder is 36 inches long and the topmost rung is 24 inches long. If the ladder has 18 rungs, how many inches each other rung is shorter than the rung below it. How many feet of wood was used in making the rungs?

Correct answer:

d =  0.7059 inch
t =  45 ft

Step-by-step explanation:

$$\begin{gathered} n=18 \\ {a}_1=24\text{ inch } \\ {a}_{18}=36\text{ inch } \\ {a}_{18}=a_1+(n-1)\cdot d \\ d={\displaystyle \frac{a_{18}-a_1}{n-1}}={\displaystyle \frac{36-24}{18-1}}={\displaystyle \frac{12}{17}}\text{ inch}=0.7059\text{ inch} \end{gathered}$$

$$\begin{gathered} s=n\cdot {\displaystyle \frac{a_1+a_{18}}{2}}=18\cdot {\displaystyle \frac{24+36}{2}}=540\text{ inch } \\ t=s\to \text{ ft}=s\mathrm{/}12\text{ ft}=540\mathrm{/}12\text{ ft}=45\text{ ft} \end{gathered}$$

Try another example

Related math problems and questions:

• Michael 2
  Michael has a 35 foot ladder leaning against the side of his house. If the bottom of the ladder is 21 feet away from his house, how many feet above the ground does the ladder touch the house?
• A 36
  A 36 g sample of the substance contains 91% water. After drying, the weight of the sample was reduced to 18 g. What percentage of water is now in the sample?
• Cross road
  From the junction of two streets that are perpendicular to each other, two cyclists (each on another street) walked out. One ran 18 km/h and the second 24 km/h. How are they away from a) 6 minutes, b) 15 minutes?
• Chickens and rabbits
  In the yard were chickens and rabbits. Together they had 18 heads and 56 legs. How many chickens and how many rabbits were in the yard?
• The raw
  The raw data presented here are the scores (out of 100 marks) of a market survey regarding the acceptability of new product launched by a company for random sample of 50 respondents: 40 45 41 45 45 30 30 8 48 25 26 9 23 24 26 29 8 40 41 42 39 35 18 25 35
• In the 8
  In the A. P. 36, 39, 42, …, which term is 276?
• Reservoir 3
  How many cubic feet of water is stored in the reservoir that has a length of 200 feet, a width of 100 feet, an overflow depth of 32 feet, and a current water level of 24 feet?
• Aquarium height
  How high does the water in the aquarium reach, if there are 36 liters of water in it? The length of the aquarium is 60 cm and the width is 4 dm.
• Martin
  Martin is making a model of a Native American canoe. He has 5 1/2 feet of wood. He uses 2 3/4 feet for the hull and 1 1/4 feet for a paddle. How much wood does he have left? Martin has feet of wood left.
• Three resistors
  You have to connect three identical resistors with 12 Ohm resistances so that you gradually get the resulting resistance a) 36 Ohm, b) 4 Ohm, 18 Ohm. Draw a diagram of each circuit.
• Find the 19
  Find the 1st term of the GP ___, -6, 18, -54.
• A bug
  A bug was sitting on the tip of a wind turbine blade that was 24 inches long when it started to rotate. The bug held on for 5 rotations before flying away. How far did the bug travel before it flew off? Exact answer.
• HP - harmonic progression 2
  Compute the 16th term of the HP if the 6th and 11th term of the harmonic progression are 10 and 18 respectively.
• RWY
  Calculate the opposite direction of the runway 13. Runways are named by a number between 01 and 36, which is generally one tenth of the azimuth of the runway's heading in degrees: a runway numbered 09 points east (90°), runway 18 is south (180°), runway 2
• Cinema
  How many rows of seats are in the stands, if you know that the first row has 24 seats and the last 50 seats and each subsequent row has two seats more than the row before? How many seats are in the stands?
• Speed of Slovakian trains
  Rudolf decided to take the train from the station 'Ostratice' to 'Horné Ozorovce'. In the train timetables found train Os 5409 : km 0 Chynorany 15:17 5 Ostratice 15:23 15:23 8 Rybany 15:27 15:27 10 Dolné Naštice 15:31 15:31 14 Bánovce nad Bebravou 15:35 1
• The perimeter of the rectangle
  The length, l, of a rectangle is 4 inches greater than its width, w. The perimeter of the rectangle is at least 30 inches. What inequality shows the range of possible widths of the rectangle?