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The current world record holder in both the 5000 m and 10000 m
is the Ethiopian runner Kenenisa Bekele. In his career he won
3 Olympic gold medals and 5 world championships.
His world record times are: e 12 min 37.35 s for 5000 m
e 26 min 17.53 s for 10000 m.
a Kenenisa’s tactic in the 5000 m was to run at a constant speed
of 6.5 msâ„¢! for most of the race, then sprint the last section at
7.7 ms~!. How far did Kenenisa sprint at the end?
b In the 10000 m, Kenenisa was not able to run quite as fast. He
ran at 6.3 ms—! for most of the race, then sprinted at 7.5 ms~*
at the end. At what point did Kenenisa sprint in this race?
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(a) Let d be "How far did Kenenisa sprint at the end",
the unknown value under the problem's question.
In other words, d is the distance, which Kenenisa Bekele ran at the speed 7.7 m/s.
Notice that 12 min 37.75 seconds = 12*60 + 37.75 = 757.75 seconds.
Then we can write this "time" equation
+ = 757.75 seconds.
To solve it, multiply both sides by the product 6.5*7.7. You will get
7.7*(5000-d) + 6.5*d = 757.75*6.5*7.7.
Simplify and find "d"
7.7*5000 - 7.7d + 6.5d = 37925.3875
-1.2d = 37925.3875 - 7.7*5000
-1.2d = -574.6125
d = = 478.84375 meters.
ANSWER. At the end, Kenenisa ran 478.84 meters (rounded) at the speed of 7.7 m/s.
Solved.
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Solve the second problem in the same way,
since the second problem is a TWIN of the first one.