Athletic race

In a race, the second-place finisher crossed the finish line 1 1/3 minutes after the first-place finisher. The third-place finisher was 1 3/4 minutes behind the second-place finisher. The third-place finisher took 34 2/3 minutes.
How long did the first-place finisher take?

Correct answer:

a =  31.5833 min

Step-by-step explanation:

$$\begin{gathered} c=34{\displaystyle \frac{2}{3}}=34+{\displaystyle \frac{2}{3}}={\displaystyle \frac{34\cdot 3+2}{3}}={\displaystyle \frac{104}{3}}\doteq 34.6667\text{ min } \\ {t}_2=1{\displaystyle \frac{3}{4}}=1+{\displaystyle \frac{3}{4}}={\displaystyle \frac{1\cdot 4+3}{4}}={\displaystyle \frac{7}{4}}=1.75\text{ min } \\ b=c-t_2=34.6667-1.75={\displaystyle \frac{395}{12}}\doteq 32.9167\text{ min } \\ {t}_1=1{\displaystyle \frac{1}{3}}=1+{\displaystyle \frac{1}{3}}={\displaystyle \frac{1\cdot 3+1}{3}}={\displaystyle \frac{4}{3}}\doteq 1.3333\text{ min } \\ a=b-t_1=32.9167-1.3333={\displaystyle \frac{379}{12}}\text{ min}=31\frac{7}{12}\text{ min}=31.5833\text{ min} \end{gathered}$$

Try another example

Related math problems and questions:

• Emily
  Emily had 20 minutes to do a three-problem quiz. She spent 11 3/4 minutes on question A and 5 1/2 minutes on question B. How much time did she have left for question C?
• Athletic race
  Before a race, you start 4 5/8 feet behind your friend. At the halfway point, you are 3 2/3 feet ahead of your friend. What is the change in distance between you and your friend from the beginning of the race?
• Clock mathematics
  If it is now 7:38 pm, what time will it be in 30,033,996,480 minutes from now?
• Free time
  Anita had 2 1/4 hours of free time in the afternoon. She spent 2/3 of her free time playing sports and watched TV for 30 minutes. How much time did she have left to read the book? Express the result as fractions of hours and numbers in minutes.
• Fractions and mixed numerals
  (a) Convert the following mixed numbers to improper fractions. i. 3 5/8 ii. 7 7/6 (b) Convert the following improper fraction to mixed number. i. 13/4 ii. 78/5 (c) Simplify these fractions to their lowest terms. i. 36/42 ii. 27/45 2. evaluate following ex
• Relay-race
  Kate ran 170 meters at 29.8 seconds, Suzan at 29.3 seconds, Roza at 34 seconds and Žofka at 30.4 seconds. How long took to run 4x170 m relay-race?
• Arelli
  Arelli had 20 minutes to do a three-problem quiz. She spent 9 7/10 minutes on question A and 3 2/5 minutes on question B. How much time did she have left for question C? Solve on paper to find the answer as a fraction.
• A turtle
  A turtle is 20 5/6 inches below the surface of a pond. It dives to a depth of 32 1/4 inches. What is the change in the turtle’s position? Write your answer as a mixed number.
• Trams
  Two trams started at the same time from the same place. One tram journey takes 30 minutes and the second 45 minutes to its final stop. How long will trams meet again?
• Ships
  Red ship begins its circuit every 30 minutes. Blue boat begins its circuit every 45 minutes. Both ships begin their sightseeing circuit in the same place at the same time always at 10:00 o'clock. a / What time does meet boat again? b / How many times a da
• Two ribbons
  The total length of the two ribbons is 13 meters. If one ribbon is 7 and 5/8 meters long, what is the length of the other ribbon?
• Three lines
  At 6 am, three bus lines are departing from the station. The first line has an interval of 24 minutes. The second line has an interval of 15 minutes. The third line runs at regular intervals of more than 1 minute. The third line runs at the same time as t
• Aman
  Aman, Anna and Tina are participating in the school race. Anna completes a lap in 120 minutes, Aman completes a lap in 240 minutes and Tina completes a lap in 60 minutes. If they all started at the same time, then after how long will they meet again?
• Time
  Write time in minutes rounded to one decimal place: 3 h 48 m 45 s.
• Paralympics
  Milan competed in the paralympics. He finished as the winner with a time of 4 minutes 37 seconds. The competitor in second place was 53 seconds slower. What time had the competitor in second place?
• Bus vs train
  Milada took the bus and the journey took 55 minutes. Jarmila was 1h 20 min by train. They arrived in Prague at the same time 10h45 min. At what time did each have to go out?
• Lunch
  Jane eats whole lunch for the 30 minutes. Which part of the lunch is eaten in 180 seconds?