Dead Heat in Race Explained with Speed and Time Examples
Dead Heat in Race means two runners finish at the same time. The required speed ratio is found from the distances covered in equal time. This page explains head-start formulas, time advantages, race leads, solved numerical examples and shortcuts used in speed, time and distance aptitude problems.
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What Is Dead Heat in a Race?
If a race is D metres long and A gives B a head start of h metres, then A covers D metres while B covers D − h metres. For a dead heat, the speed ratio is A:B = D:(D − h). For example, in a 200 m race, if A gives B a 20 m start, their speed ratio is 200:180 = 10:9.
Dead Heat in Race Video Lessons
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Race Problems: Head Start and Dead Heat
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Dead Heat in Race Formula & Tricks
Important Formulas
In a D-metre race, if A gives B a head start of h metres and they finish together, A covers D and B covers D − h.
If the speeds are in the ratio A:B and A gives B a head start, then D:(D − h) = A:B. Therefore, h = D(B − A) ÷ B.
For the same race distance, speed is inversely proportional to time. If A takes t₁ seconds and B takes t₂ seconds, the speed ratio is t₂:t₁.
If B starts t seconds before A and both finish together, and A takes T seconds after starting, B runs for T + t seconds.
Quick Tricks
In a dead heat, both runners run for the same total time. Therefore, speed ratio equals distance ratio. Subtract the head start from the full race length for the slower runner's distance.
Set the full race length against the faster runner's ratio term, then calculate the distance covered by the slower runner. The difference is the head start.
When one runner starts earlier, the early starter runs for the other runner's time plus the time lead. Use speed ratio = other runner's total time : later starter's time.
Dead Heat in Race Concepts
Dead Heat with a Metre Head Start
A runs the entire distance D, while B runs only D − h because B begins h metres ahead. Since the running times are equal, speed is proportional to distance covered. Thus, speed A:speed B = D:(D − h).
Finding the Head Start from the Speed Ratio
For a dead heat, D:(D − h) = m:n. Cross-multiplication gives nD = m(D − h), so mh = D(m − n), and h = D(m − n) ÷ m. This applies when A is faster, so m > n.
Dead Heat with a Time Head Start
Let A run for T seconds. B runs for T + t seconds because B started earlier. For the same finishing distance, speed A:speed B = (T + t):T. If the speed ratio and one running time are known, the time head start follows by comparing the two running times.
Race Lead and Equivalent Dead Heat
When A finishes, B has covered only D − x metres. Therefore, in the same time, A and B cover D and D − x metres respectively. The mathematical model is identical to A giving B an x-metre start and both finishing together.
Two Successive Race Comparisons
If A beats B by x metres in a D-metre race, A:B = D:(D − x). If B beats C by y metres in the same race, B:C = D:(D − y). Multiplying these ratios gives A:C. Reduce the final ratio before finding a new lead.
Dead Heat in Race Data Table
Use the structured data below while following the explanation and examples.
Common Dead Heat Situations
The distance or time covered by each runner determines the speed ratio.
| Situation | Runner A | Runner B | Speed ratio A:B |
|---|---|---|---|
| D-metre race; B gets h-metre head start | D | D − h | D:(D − h) |
| A beats B by x metres in a D-metre race | D | D − x | D:(D − x) |
| B starts t seconds earlier; A runs for T seconds | T seconds | T + t seconds | (T + t):T |
| A and B cover equal distance in equal time | D | D | 1:1 |
Note: Use consistent units for all distances and times before applying the ratios.
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Dead Heat in Race: Revision Points
Use equal-time distance ratios to solve head-start and race-lead questions.
- Dead heat means both runners finish at the same time.
- For a D-metre race with an h-metre head start, speed ratio = D:(D − h).
- If A beats B by x metres in a D-metre race, speed ratio = D:(D − x).
- If speed ratio A:B = m:n, the head start given by A is D(m − n) ÷ m.
- For a time head start t, if A runs for T seconds, B runs for T + t seconds.
- For equal distances, speed ratio is the inverse of the time ratio.
- Keep distance units and time units consistent before calculating.
Dead Heat in Race FAQs
What is the dead heat in race formula for a metre head start?
For a D-metre race where A gives B h metres, the speed ratio is A:B = D:(D − h).
A gives B a 25 m start in a 250 m race. What is their speed ratio?
A covers 250 m and B covers 225 m. Therefore, speed ratio A:B = 250:225 = 10:9.
A and B have speeds in the ratio 5:4. What head start can A give B in a 200 m race?
Head start = 200 × (5 − 4) ÷ 5 = 40 m. A can give B a 40 m start.
If A beats B by 20 m in a 100 m race, what is the speed ratio?
When A finishes 100 m, B has covered 80 m. Thus, speed ratio A:B = 100:80 = 5:4.
How is a time head start used in a dead heat problem?
Add the time head start to the later runner's running time to get the early starter's time. If A runs for T seconds and B starts t seconds earlier, the times are T and T + t.
A completes a race in 24 seconds and B starts 6 seconds earlier. What is the speed ratio if they finish together?
B runs for 24 + 6 = 30 seconds. Hence speed A:B = 30:24 = 5:4.