Linear Races

Linear Races :- when we have straight tracks for races.

Terms used to define linear races & their actual meanings:-

A gives B a start of 10 meters : B starts a race 10 meters ahead of A.

A gives B a start of 10 seconds : B starts 10 seconds before A.

A beats B by 10 meters : When A reaches finishing line, B is 10 meters behind.

A beats B by 10 seconds : B takes 10 seconds more than A to finish race.

A beats B by 10 meters or 10 seconds: B takes 10 seconds to cover 10 meters. Speed of B is 1 m/s.

Beat time : difference between time take by loser & winner.

Winner's distance: Length of the race track. 

Time take by winner =  time taken by loser - beat time.

Dead Heat : Tie 

Q1. X beats Y by 60 meters or by 12 seconds in a 2 Km race.Find Speed of X, Speed of Y, Time taken by X & time taken by Y.

Solution:-

Speed of Y = 60 / 12 = 5 m/s

Time taken by Y = 2000 / 5 = 400 minutes

Time taken by X = 400 - 60 = 340 minutes
Speed of X = 2000 / 340 = 5.88 m/s


Q2. In a 1000 m race, Neeta beats Geeta by 50 m & Seeta by 100 m. By what distance will Geeta beat Seeta ?
(1) 48.36 m (2) 50 m(3) 52.64 m (4) 51.28 m (5) 52.36 m


Solution :-
Distance covered by Neeta : Geeta in winning time by Neeta is = 1000 : 950 = 20:19.

Since time taken is same, ratio of their speed is also 20:19
Distance covered by Neeta : Seeta in winning time by Neeta is = 1000 : 900 = 20:18.
Since time taken is same, ratio of their speed is also 20:18
Hence Ratio of speeds of Geeta to Seeta would be 19:18.

Distance covered by Seeta when Geeta covers 1000 m = 1000 * 18/19 = 947.36
So Geeta beats Seeta by 1000 - 947.36 = 52.64 m. Hence answer option 3.


Q3. M beats N by 30 m or 5 seconds. Which of the following statements is/are true ?
I. Speed of N can not be found.
II. Speed of M can be found.
III. Distance covered by N can be found. 
IV. N takes 6 more seconds to meet M.

1. Statement I is true.
2. Statement I, II & III are true.
3. Statement I & III are true.
4. All statements are true.
5. All statements are false. 

Solution:-
By given data only speed of N can be found. To find other parameters we need length of track. Hence no statement is true. So answer option 5. 

Q4. A gives B a start of 15 seconds. A can run at speed of 80 mps & B can run at speed of 40 mps. In how much time will A  meet B on straight track after B starts race?
(1) 10 s (2) 12 s(3) 15 s  (4) 20 s (5) 30 s

Solution:-
Distance covered by B in early 15 seconds = 40 * 15 = 600 m
Relative speed of A & B = 80 - 40 = 40 mps
Time taken after A begin = 600 / 40 = 15 seconds.
Total time after B begins race = 15 + 15 = 30 seconds.Hence answer option 5. 

Q5. In above question, what would have been speed of A so that it would meet B after 2 mins after B begins his race ? (All other data remains same)
(1) 42.52 m/s(2) 45 m/s (3) 45.15 m/s (4) 45.71 m/s (5) 50 m/s

Solution:-
Relative Distance = 600 meters.
Time = 120 - 15 = 105 seconds
Relative Speed = 600 / 105 = 5.71 m/s
Speed of A = 40 + 5.71 = 45.71 m/s
-----------------------------------------------------------------------------------------------------------------
Go back to concepts to learn more-> click here