# Science/Math

Word Problem page 19

John and Al are in a 15 km race. John averages 4.4 m/s during the first half of the race and then runs at a speed of 4.2 m/s until the last 200 m, which he covers at 4.5 m/s. At what average speed must Al run to beat John?

The textbook that included the word problem is: Basic Biomechanics Sixth Edition by Susan J. Hall;
ISBN#978-0-07-337644-8

The course name: Biomechanics

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1. We don't have your textbooks, all our help is not dependent on any texts.

We have to know how long it took for John to run the 15 km
He did the first half at 4.4 m/s, so
time for first half = 7500 / 4.4 second or 18750/11 seconds
next leg is 7300 m at 4.2 m/sec, takes 36500/21 seconds
last stretch is 200 m at 4.5 m/s takes 400/9 sec
total time = 18750/11 + 36500/21 + 400/9
= 3487.085 seconds

so Al must run at 15000/3487.085 m/s
which is 4.3 m/s to be even with him
So to beat John , Al must run faster than 4.3 m/s

(practically speaking John runs half the race at 4.4 m/s and the other "half" (200 m less) at 4.2 m/s
so the average speed of 4.3 m/s is quite logical)

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