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 answer:

x =  117 km

Step-by-step explanation:

$$\begin{gathered} a_1=18\text{ km } \\ q=90\mathrm{\%}={\displaystyle \frac{90}{100}}=0.9 \\ {a}_2=a_1\cdot q=18\cdot 0.9={\displaystyle \frac{81}{5}}=16.2\text{ km } \\ {a}_3=a_2\cdot q=16.2\cdot 0.9={\displaystyle \frac{729}{50}}=14.58\text{ km } \\ \dots \\ n=10 \\ x=a_1\cdot {\displaystyle \frac{q^n-1}{q-1}}=18\cdot {\displaystyle \frac{0.9^{10}-1}{0.9-1}}=117\text{ km} \end{gathered}$$

Try another example

Related math problems and questions:

• Scouts
  The boys from scout group traveled 5 days distance 115 km. Every day walked 1.5 km less than the previous day. How many kilometers scouts walked in the first day?
• Three-day trip
  The cyclist on three-day trip travel 30% of the total route on the first day, 3/5 of the rest on the second day and 35 km on the third day. How many kilometers did travel cyclists each day and how many?
• The hiker
  The hiker will travel 40% of the route on the first day 1and/3 of the rest of the second day. Last day 30 km. What was the length of the 3-day trip? How many kilometers did he walk each day?
• Paddlers
  Students of canoeists trip traveled in three days 102 km. Second day traveled 15% more than first day and at the third day 9 km over the second day. How many kilometers traveled each day?
• Scouts
  Three scouts went on a three day trip. The second day went 4 km more than the first day. The third day went two times less than the first day. They went along 54 km. How many kilometers went every day together?
• Cyclo trip
  Eighth-graders took a full-day trip on a cycling course. They took 1/7 of the route to the first break and added another 3/7 of the route to lunch. They had 18 km left to the finish. How many kilometers did the trip route measure?
• Car
  Car is traveling 95 km per hour. How long-distance it travel in 1 minute?
• 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?
• Car and motorcyclist
  A car and a motorcyclist rode against each other from a distance of 190 km. The car drove 10km/h higher than the motorcyclist and started half an hour later. It met a motorcyclist in an hour and thirty minutes. Determine their speeds.
• Cycling
  Cyclist goes on a trip. First, drove 4 hours average speed 44 kilometers per hour, then slowed down and another 4 hours driving a speed 36 kilometers per hour. How many total kilometers cycling?
• The tourist
  The tourist traveled 190km in 5 hours. Part of the journey passed at 5 km/h. The rest he went by bus at a speed of 60 km/h. How long has a bus going?
• Grandmother
  Mom walked out to visit her grandmother in a neighboring village 5km away and moved at a speed of 4km/h. An hour later, father drove down the same road at an average speed of 64km/h. 1) How long will take to catch mom die? 2) What is the approximate dista
• Motion 2
  At 10 o'clock started from place A car speed at 90 km/h. 20 minutes after started from the place B at speed 60 km/h another car. Distance places A and B is 120 kilometers. What time and where they meet?
• Pedestrian and cyclist
  Pedestrian out with a speed of 4 km/hour from city center and after 1hour and 10 minutes came after him cyclist at speed of 18 km/h. At how many minutes he catches up with pedestrian?
• Train
  The train is running at speeds of 96 km/h. From the beginning of braking to full stop train run for 3.3 minutes. If the train slows the braking equally, calculate the distance from the location where you need to start to brake.
• Cyclist
  Cyclist rode two-fifths of the way the first day. The second day drove 5 km less while traveled three-eighths of route. How many kilometers does he have to finish target?
• The tourist
  The tourist traveled 78km in 3 hours. Part of the journey went on foot at 6km/h, the rest of the trip by bus at 30km/h. How long did he walk?