Hello, joyiu!

This can be solved without Alger=bra ... just some serious Thinking.

have a 1500-meter race.

beats by 30 meters and by 100 meters.

By how much would beat over the full distance

. . if they both ran as before?

When ran 1500 meters:

. . ran only 1470 meters,

. . and ran a mere 1400 meters.

Hence, speed is only of speed.

When runs 1500 meters,

. . runs only: . meters.

Therefore, beats by about: meters.