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In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:
- a)60 m
- b)20 m
- c)40 m
- d)10 m
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In a 500 m race, the ratio of the speeds of two contestants A and B is...
To reach the winning point , A will have to cover a distance of 500 – 140= 360 metre ratio of the speeds of two contestants A and B is 3 : 4
i.e., when A covers 3 metre, B covers 4 metre.
=> When A covers 360 metre, B covers 43×360 = 480 metre.
Remaining distance B have to cover = 500-480= 20 metre
=> A wins by 20 metre
i.e., when A covers 3 metre, B covers 4 metre.
=> When A covers 360 metre, B covers 43×360 = 480 metre.
Remaining distance B have to cover = 500-480= 20 metre
=> A wins by 20 metre
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In a 500 m race, the ratio of the speeds of two contestants A and B is...
Understanding the Problem
In a 500 m race, contestant A has a speed ratio of 3 compared to contestant B's speed of 4. A also has a head start of 140 m. We need to determine how much A wins by after completing the race.
Calculating Distances and Times
- Distance Covered by A:
A runs 500 m - 140 m = 360 m.
- Speed Ratios:
Let the speeds of A and B be 3x and 4x respectively.
Calculating Time Taken
- Time for A to Complete the Race:
Time = Distance / Speed
Time taken by A = 360 / 3x = 120 / x.
- Distance Covered by B in the Same Time:
In the time A takes to finish, B covers:
Distance = Speed × Time
Distance covered by B = 4x × (120 / x) = 480 m.
Determining the Outcome
- Total Length of the Race:
The race is 500 m long.
- Remaining Distance for B:
Since B covers 480 m, he has:
Remaining distance = 500 m - 480 m = 20 m.
Conclusion
A wins the race by the distance that B has left to cover, which is 20 m. Thus, the correct answer is option 'B' - A wins by 20 m.
In a 500 m race, contestant A has a speed ratio of 3 compared to contestant B's speed of 4. A also has a head start of 140 m. We need to determine how much A wins by after completing the race.
Calculating Distances and Times
- Distance Covered by A:
A runs 500 m - 140 m = 360 m.
- Speed Ratios:
Let the speeds of A and B be 3x and 4x respectively.
Calculating Time Taken
- Time for A to Complete the Race:
Time = Distance / Speed
Time taken by A = 360 / 3x = 120 / x.
- Distance Covered by B in the Same Time:
In the time A takes to finish, B covers:
Distance = Speed × Time
Distance covered by B = 4x × (120 / x) = 480 m.
Determining the Outcome
- Total Length of the Race:
The race is 500 m long.
- Remaining Distance for B:
Since B covers 480 m, he has:
Remaining distance = 500 m - 480 m = 20 m.
Conclusion
A wins the race by the distance that B has left to cover, which is 20 m. Thus, the correct answer is option 'B' - A wins by 20 m.
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