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marathon is a race of approximately 42 km. In many marathon
A
there is a relay category in which a team of runners
competitions,
together to complete the race, with each competitor running
works
portion of the entire distance.
some
Suppose three friends create a relay team and, because of their
a
abilities, they decide to run distances in a ratio of 1 : 2 :
diering
After the rst 2 km, the rst runner injures himself. The remaining
b
runners decide to run the rest of the race in a ratio of 3 : 5.
two
Runner 2’s portion = 2 6 or 1 3
Runner 3’s portion = 3 6 or 1 2
Runner 1’s portion = 1 6
Runner 2’s portion = 1 3
Runner 3’s portion = 1 2
7 km + 14 km + 21 km = 42 km ✓
runner will run 7 km, another 14 km and the
One
one 21 km.
third
8r = 40
r = 5
each runner’s contribution as a fraction
Express
the total.
of
the fraction of the race run by each
Calculate
runner.
the 2 km mark, there are 40 km remaining in
At
race. The goal is to nd a ratio equivalent to
the
if you multiply each of the values by the
Thus,
constant, then that should sum to 40.
same
Example 2
Q
3. How far does each person run?
How far did the remaining two competitors run?
A
a 1 + 2 + 3 = 6
Find the total of the number of terms in the ratio.
Runner 1’s portion = 1 6
1
or ×
of 42 = 7
42,
6
1
42, or × = 42 14
of
3
1
42 21
of 42, or × =
2
Check your solution to make sure it works.
b Find a ratio equivalent to 3 : 5
3 : 5 where the values sum to 40.
3r : 5r
3r + 5r = 40
Simplify the left-hand side and solve.
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1 Ratios and proportions
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