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Assuming that the sprinter could keep running at the same speed for 1 mile, then:

1 minute = 60 seconds

1 yd = 0.9144 m (exactly)

1 mile = 1760 yd = 1760 × 0.9144 m = 1609.344 m

100m in 10 secs is speed = 100/10 m/s = 10 m/s

→ 1 mile at 10 m/s takes: 1609.344 m / 10 m/s = 160.9344 seconds ≈ 161 seconds

→ 161 secs = 161 ÷ 60 mins = 2 mins 41 seconds (just over 2 2/3 mins).

The assumption is not a realistic one:

Sprinters are not endurance runners and although they can cover a short distance in a quick time, over a longer distance they (nor can anyone else) cannot keep up that speed: The current world records are:

100 m - 9.58 s (Usain Bolt)

200 m - 19.19s (Usain Bolt)

400 m - 43.18s (Michael Johnson)

800 m - 100.91s (David Rudisha)

1 mile - 223.13s (Hicham El Guerrouj)

If Usain Bolt could keep his sprinting speed up for the whole of all those distances his times would be:

200 m - 19.16s (0.03s faster)

400 m - 38.32s (4.86s faster)

800 m - 76.64s (24.27s faster)

1 mile - 154.17s (68.96s or 1 min 8.96 sec faster).

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Q: If an Olympic runner runs 100 meters in 10 seconds how fast can that same sprinter run one mile?
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