Hiking trip

Rosie went on a hiking trip. The first day she walked 18kilometers. Each day since she walked 90 percent of what she walked the day before. What is the total distance Rosie has traveled by the end of the 10th day?
Round your final answer to the nearest kilometer.

Correct result:

x =  117 km

Solution:

a1=18 km q=90%=90100=0.9  a2=a1 q=18 0.9=815=16.2 km a3=a2 q=16.2 0.9=72950=14.58 km ... n=10  x=a1 qn1q1=18 0.91010.91=117 kma_{1}=18 \ \text{km} \ \\ q=90 \%=\dfrac{ 90 }{ 100 }=0.9 \ \\ \ \\ a_{2}=a_{1} \cdot \ q=18 \cdot \ 0.9=\dfrac{ 81 }{ 5 }=16.2 \ \text{km} \ \\ a_{3}=a_{2} \cdot \ q=16.2 \cdot \ 0.9=\dfrac{ 729 }{ 50 }=14.58 \ \text{km} \ \\ ... \ \\ n=10 \ \\ \ \\ x=a_{1} \cdot \ \dfrac{ q^n-1 }{ q-1 }=18 \cdot \ \dfrac{ 0.9^{10}-1 }{ 0.9-1 }=117 \ \text{km}



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
Our percentage calculator will help you quickly calculate various typical tasks with percentages.
Do you want to convert length units?
Do you want to convert velocity (speed) units?
Do you want to round the number?

Next similar math problems:

  • The hiker
    tourist The hiker will travel 40% of the route on the first day 1and/3 of the rest od second day. Last day 30 km. What was the length of the 3-day trip? How many kilometers did he walk each day?
  • A trip to the peak Dry
    Suchy Calculate what percentage is rising trip from Strečno to peak Suchý (Dry peak) longer than the descent back. Team trio of tourists (Palo, Peter and Andrew) rise took 4:21 and descent 3:08.
  • Six terms
    sequence_geo_3 Find the first six terms of the sequence a1 = -3, an = 2 * an-1
  • A perineum
    sequence_geo_9 A perineum string is 10% shorter than its original string. The first string is 24, what is the 9th string or term?
  • Five members
    pst3.JPG Write first 5 members geometric sequence and determine whether it is increasing or decreasing: a1 = 3 q = -2
  • Geometric sequence 4
    Koch_Snowflake_Triangles It is given geometric sequence a3 = 7 and a12 = 3. Calculate s23 (= sum of the first 23 members of the sequence).
  • The position
    motion2_3 The position of a body at any time T is given by the displacement function S=t3-2t2-4t-8. Find its acceleration at each instant time when the velocity is zero.
  • Researchers
    house Researchers ask 200 families whether or not they were the homeowner and how many cars they had. Their response was homeowner: 14 no car or one car, two or more cars 86, not homeowner: 38 no car or one car, two or more cars 62. What percent of the families
  • UV radiation
    uv_rays The glass of 1 mm thickness absorb 4% of UV radiation passing through. How many percent of UV rays absorb glass with a thickness 1.1 cm, made from 1 mm thick those glasses?
  • Geometric progression 2
    exp_x There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.
  • Piano
    piano If Suzan practicing 10 minutes at Monday; every other day she wants to practice 2 times as much as the previous day, how many hours and minutes will have to practice on Friday?
  • Geometric progression
    fractal Fill 4 numbers between 4 and -12500 to form geometric progression.
  • Wavelength
    wave_length Calculate the wavelength of the tone frequency 11 kHz if the sound travels at speeds of 343 m/s.
  • Hot air balloon
    balon Hot air balloon ascends 25 meters up for a minute after launch. Every minute ascends 75 percent of the height which climbed in the previous minute. a) how many meters ascends six minutes after takeoff? b) what is the overall height 10 minutes after launch
  • Tenth member
    10 Calculate the tenth member of geometric sequence when given: a1=1/2 and q=2
  • Five harvests
    zrno In the seed company, they know that, out of 100 grains of a new variety, they get an average of 2000 grains after harvest. Approximately how many grains do they get out of 100 grains after five harvests?
  • JUDr. Usury
    paragraph Judge JUDr. Usury approved the agreement on guilt and punishment where confessed to pay daily interest 0.18%. How big is a yearly interest? Year has 360 days.