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Algebra Difficulty 1.5 Junior Find the answer Canada

Natascha cycles 3 times as fast as she runs. She spends 4 hours cycling and 1 hour running. The ratio of the distance that she cycles to the distance that she runs is

$12:1$
$7:1$
$4:3$
$16:9$
$1:1$

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Suppose that Natascha runs at $r$ km/h.

Since she cycles 3 times as fast as she runs, she cycles at $3r$ km/h.

In 1 hour of running, Natascha runs $\text{(1 h ) (r km/h ) = r km}$ .

In 4 hours of cycling, Natascha cycles $\text{(4 h ) (3r km/h ) = 12r km}$ .

Thus, the ratio of the distance that she cycles to the distance that she runs is equivalent to the ratio $\text{12r km : r km}$ which is equivalent to $12:1$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.