P can give Q a start of 20 seconds in a kilometer race. P can give R a start of 200 meters in the same kilometer race. And Q can give R a start of 20 seconds in the same kilometer race. How long does P take to run the kilometer?
P can give Q a start of 20 seconds in a kilometer race. So, if Q takes 'x' seconds to run a
kilometer, then P will take x â€“ 20 seconds to run the kilometer.
Q can give R a start of 20 seconds in a kilometer race. So, if R takes 'y' seconds to run a
kilometer, then Q will take y â€“ 20 seconds to run the kilometer.
We know Q takes x seconds to run a kilometer
Therefore, x = y â€“ 20
Therefore, P will take x â€“ 20 = y â€“ 20 â€“ 20 = y â€“ 40 seconds to run a kilometer.
i.e. P can give R a start of 40 seconds in a kilometer race, as R takes y seconds to run a kilometer
and P takes only y â€“ 40 seconds to run the kilometer.
We also know that P can give R a start 200 meters in a km race.
This essentially means that R runs 200 meters in 40 seconds.
Therefore, R will take 200 seconds to run a km.
If R takes 200 seconds to run a km, then P will take 200 â€“ 40 = 160 seconds to run a km.
Workspace
NA
SHSTTON
4
Solv. Corr.
10
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14
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2 / 6
Choose the correct option.
A takes 3 min 45 seconds to complete a kilometre. B takes 4 minutes to complete the same 1 km track. If A and B were to participate in a race of 2 kms, how much start can A give B in terms of distance?
A can give B a start of 15 seconds in a km race.
B takes 4 minutes to run a km. i.e 1000/4= 250 m/min = 250/60 m/sec
Therefore, B will cover a distance of = 62.5 meters in 15 seconds.
The start that A can give B in a km race therefore, is 62.5 meters, the distance that B run in 15 seconds.
Hence in a 2 km race, A can give B a start of 62.5 * 2 = 125 m or 30 seconds.
Workspace
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8
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25
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Choose the correct option.
In a 200 m race, A beats B by 20 m and c by 38m. In a race of 600 m B will beat C by
It means, when A covers 200 m,
B covers only (200-20)=180 m
and C covers only (200-38)=162 m
=> When C covers 162 m, B covers 180 m
=> When B covers 600 m, C covers (162/180) * 600 = 540 m
Hence, B beats C by (600-540) = 60 metre
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Anusha, Banu and Esha run a running race of 100 meters. Anusha is the fastest followed by Banu and then Esha. Anusha, Banu and Esha maintain constant speeds during the entire race. When Anusha reached the goal post, Banu was 10m behind. When Banu reached the goal post Esha was 10m behind. How far was behind Anusha when the latter reached the goal post.
By that time Anusha covered 100m, Bhanu covered 90m. So ratio of their speeds = 10 : 9 By that time Bhanu reached 100m, Esha covered 90m. So ratio of their speeds = 10 : 9 Ratio of the speed of all the three = 100 : 90 : 81
By that time Anusha covered 100m, Esha Covers only 81.
Workspace
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Choose the correct option.
Alvin, Ben and Clinton run a race, with Alvin finishing 48 meters ahead of Ben and 72 meters ahead of Clinton, while runner Ben finishes 32 meters ahead of runner Clinton. Each runner travels the entire distance at constant speed. What is the length of the race?
Let us assume the speeds of alvin,ben,clinton = A,B,C resp.
and the length of race = d
let in time t alvin finishes the race
A*t=d
B*t=d-48 ------- (1)
C*t=d-72 --------(2)
So,B:C=(d-48):(d-72) ------- (3)
Now Ben covers 48 mt more to complete the race.
In the same time Clinton covers 40mt (as it is given that he is beaten by 32mt by ben)
So,B:C=48:40....(4) (speed proportional to distance covered if time is same)
By, comparing equation (3) and (4)
d=192 mt
Workspace
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4
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In a 10 km race, A, B, and C, each running at uniform speed, get the gold, silver, and bronze medals, respectively. I f A beats B by 1 km and B beats C by 1 km, then by how many metres does A beat C?
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