Athletic oval

On the 400 m athletic oval, two athletes started back to back from the same level. After the starting shot, they both ran away from each other at the same time. Athlete A ran at 15 km/h, and Athlete B ran at 17 km/h. A) in how many seconds did the athletes meet each other? B) how many meters did each athlete run before they met?

Correct result:

t =  45 s
s₁ =  187.5 m
s₂ =  212.5 m

Solution:

$$\begin{gathered} s=400\text{ m } \\ {v}_1=15\text{ km/h}\to \text{ m/s}=15\mathrm{/}3.6\text{ m/s}=4.16667\text{ m/s } \\ {v}_2=17\text{ km/h}\to \text{ m/s}=17\mathrm{/}3.6\text{ m/s}=4.72222\text{ m/s } \\ t={\displaystyle \frac{s}{v_1+v_2}}={\displaystyle \frac{400}{4.1667+4.7222}}=45\text{ s} \end{gathered}$$

$s_1=v_1\cdot t=4.1667\cdot 45={\displaystyle \frac{375}{2}}=187\frac{1}{2}={\displaystyle \frac{375}{2}}\text{ m}=187.5\text{ m}$

$s_2=v_2\cdot t=4.7222\cdot 45={\displaystyle \frac{425}{2}}=212\frac{1}{2}={\displaystyle \frac{425}{2}}\text{ m}=212.5\text{ m}$

Try another example

Showing 0 comments:

Related math problems and questions:

• Two trains meet
  From A started at 7:15 express train at speed 85 km/h to B. From B started passenger train at 8:30 in the direction to A and at speed 55 km/h. The distance A and B are 386 1/4 km. At what time and at what distance from B the two trains meet?
• 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?
• Motion
  From two different locations distant 232 km started against car and bus. The car started at 5:20 with average speed 64 km/h. Bus started at 7:30 with average speed 80 km/h. When they meet? How many kilometers went the bus?
• Two ships
  The distance from A to B is 300km. At 7 am started from A to B a ferry with speed higher by 20 km/h than a ship that leaves at 8 o'clock from B to A. Both met at 10h 24min. Determine how far they will meet from A and when they reach the destination.
• 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?
• Two trains
  Two trains go at each other. First at speed 40 km/h and the second at speed 60 km/h. At what distance will be 30 minutes before they will meet?
• Two cities
  Cities A and B are 200 km away. At 7 o'clock from city A, the car started at an average speed of 80 km/h, and from B at 45 min later the motorcycle is started at an average speed of 120 km/h. How long will they meet and at what distance from the point A i
• Cars motion
  From point A car start at the speed of 90 km/h. Against it departs from the point B at the same time another car at 60 km/h. For how long and where they met if the distance between A and B is 180 km?
• Dog
  Man goes with a dog on a long walk 17 km from the house. Man is walking at speed 4.9 km/h and a dog that constantly running between house and man at 12.6 km/h. How many kilometers will run the dog when they reach their destination?
• Train from Prague
  First train from Prague started at 8:00 hour at 40 kilometers per hour. Train from Ostrava started at 9:20 at 80 km per hour. In how many hours and how far from cities with trains meet if the distance of cities is 400 km.
• Against each other
  From two points A, B distant 23 km at the same time started two cars against each other at speeds 41 km/h and 65 km/h. How long does cars meet and what distance passes each of them?
• Hiker and cyclist
  At 7 PM hiker started at 6 km/h to hike. After 3 hrs. later started on the same trip cyclist at speed of 15 km/h. After an hour of driving a flat tire and take him half hours to correct defect. At what time catch up cyclist with hiker?
• Cenda and Pepa
  Cenda and Pepa went to the event. Cenda started alone. Canda started after him for 20 minutes. How long took Cenda to catch him? Cenda traveling at 15 km/h, and Pepa traveling at 25 km/h.
• Cars
  Cars started at 7:00 AM. From point A car run at 40 km per hour, from B car run 70 km per hour. Between A and B is 250 km long road. When and where will meet (measured from point A)?
• 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.
• Fly and cyclist
  Two cyclists are at 20 km apart on a same line. They start at same time towards each other at a speed of 10 km/hr. A fly sitting on one of the cyclists handle start flying towards the other cyclists at a speed of 20 km/hr. It touches the handle and move b
• Two trains
  From station A, the freight train traveled at a speed of 40 km/h in 9h. When he drove 15km, the fast train started from station A in the same direction at a speed of 70km/h. When will it the freight train catch up?