Three roads

The three boys moved from start to finish on three different routes A, B, C, always at the same time. Adam drove road A 1500 m long on a scooter. Blake walked route B 600 m long on foot. Cyril got on a scooter on route C after a 90 m walk, then he left the scooter 60 m before the finish line and reached the finish line on foot. Adam rides a scooter as fast as Cyril. Cyril walks as quickly as Blake. We neglect time losses when getting on a scooter and putting the scooter away. Calculate how many times a scooter ride is faster than a walk. Adam and Cyril started at the same time. Express a fraction of the part of the route that Adam had followed when Cyril mounted the scooter. Calculate how many meters Cyril traveled on a scooter.

Correct result:

r =  2.5
a =  0.15
c =  1125 m

Solution:

$$\begin{gathered} s_1=1500\text{ m } \\ {s}_2=600\text{ m } \\ r=v_1:v_2 \\ r=(s_1\mathrm{/}t):(s_2\mathrm{/}t) \\ r=s_1\mathrm{/}{s}_2=1500\mathrm{/}600={\displaystyle \frac{5}{2}}=2.5 \end{gathered}$$

$$\begin{gathered} s_3=90\text{ m } \\ {s}_3=v_2\cdot t_3 \\ {s}_4=v_1\cdot t_3 \\ {s}_4=v_1\cdot (s_3\mathrm{/}{v}_2) \\ {s}_4=s_3\cdot v_1\mathrm{/}{v}_2 \\ {s}_4=s_3\cdot r=90\cdot 2.5=225\text{ m } \\ a=s_4\mathrm{/}{s}_1=225\mathrm{/}1500={\displaystyle \frac{3}{20}}=0.15 \end{gathered}$$

$$\begin{gathered} s_5=60\text{ m } \\ {s}_6=s_5\cdot r=60\cdot 2.5=150\text{ m } \\ c=s_1-s_4-s_6=1500-225-150=1125\text{ m} \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Direct route
  From two different places A and B connected by a direct route, Adam (from city A) and Bohus (from city B) started at a constant speed. As Adam continued to go from A to B, Bohus turned around at the time of their meeting and at the same speed he returned
• Exponential decay
  A tank contains 55 liters of water. Water is flowing out at the rate of 7% per minute. How long does it take to drain the tank?
• Two cars on ring
  There were two cars on the round track (ring) in the adjacent tracks, the first car in the inner track, the second in the outer track. Both cars started at the same time from one starting track. The first toy car drove every four laps simultaneously as th
• Quiz or test
  I have a quiz with 20 questions. Each question has 4 multiple choice answers, A, B, C, D. THERE IS NO WAY TO KNOW THE CORRECT ANSWER OF ANY GIVEN QUESTION, but the answers are static, in that if the "correct" answer to #1 = C, then it will always be equal
• Reconstruction of the corridor
  Calculate how many minutes will be reduced to travel 187 km long railway corridor, where the maximum speed increases from 120 km/h to 160 km/h. Calculate how many minutes will shorten travel time, if we consider that the train must stop at 6 stations, eac
• Walkers
  From points A and B simultaneously started against each other two walkers. After meeting both continue to B. Second walker came to B 2 hours before the first walker. It's speed is 2.7 times of speed of the first pedestrian. How many hours went pedestrians
• University bubble
  You'll notice that the college up slowly every other high school. In Slovakia/Czech republic a lot of people studying political science, mass media communication, social work, many sorts of management MBA. Calculate how many times more earns clever 25-yea
• Bus and Milan
  The bus started from the village at speed 60 km/h. After one kilometer, when Milan came to bus stop on a motorcycle with grandmother. When they found that bus drove away he try to catch it. At the next stop, a distance of 3km caught up bus. How quickly ha
• Candelas
  We burned two unequally thick and long candles. Longer burnt for three and a half hours and shorter for five hours. After two hours of burning it was identical. How many times was longer candle longer then shorter?
• Fog
  The car started in fog at speed 30 km/h. After a 12-minute drive, the fog dissipated and the driver drove next 12 minutes distance 17 km. On the last 17 km long again the driving conditions deteriorated and the driver drove the speed of 51 km/h. a) Calcul
• Pedestrian and the cyclist
  Pedestrian and cyclist went against each from the two cities that are distant 40 km. Pedestrian started 30 minutes before the cyclist and walk an average speed of 5 km/h. What speed went cyclist when met after 120 minutes from the start of the pedestrian?
• 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
• Motion2
  Cyclist started out of town at 19 km/h. After 0.7 hours car started behind him in the same direction and caught up with him for 23 minutes. How fast and how long went car from the city to caught cyclist?
• Overtaking
  On the direct road, the passenger car overtakes the slower bus by starting to overtake 20 meters from the bus and after passing it ahead of it again 20 meters away. The car overtakes at a steady speed of 72 km/h, the bus goes at a steady speed of 54 km/h.
• Two friends
  Peter can do all his work himself in 6 hours. Martin can do the same work himself in 8 hours. Peter worked first and then replaced by Martin. Whole work was done in 6.5 hours. Calculate how long Peter worked before replaced by Martin.
• Kaufland sales-off
  As a rule the goods to the approaching end consumption in Kaufland three days before the end of the consumption to 30% off and one day before the end of the consumption to 50% discounts. Sometimes however the seller has been mistaken and the second discou
• Moving
  Vojta left the house at three o'clockat 4 km/h. After half hour later went from the same place Filip by bicycle at speed 18 km/h. How long take Tilip to catch up Vojta and how far from the house?