Mathematics

Question

In the 2000 summer Olympics, the women’s 400-meter freestyle winner took 4 minutes 4 seconds to swim her race. The 200-meter freestyle winner took 1 minute 57 seconds. If the 400-meter winner had swum her whole race at the same average speed as the 200-meter winner, by how many seconds would she have reduced her time?

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  • Step-by-step explanation:

    so, the 200m winner's average speed was

    200m/(60+57)sec = 200/117 m/s

    so, 400m with the same speed would need x seconds :

    200x/117 = 400

    200x = 400×117

    x = 2×117 = 234 seconds = 3 minutes and 54 seconds

    (after seeing that a minute has 60 seconds, and that then 234/60 = 3 and 54 remainder).

    so, she would have reduced her time by 10 seconds (from 4 minutes 4 seconds down to 3 minutes 54 seconds = 4 + 6 = 10).