Rachel ran \(\frac{\mathrm{1} }{\mathrm{2}}\) mile in 4 minutes. At this rate, how many miles can she run in 15 minutes?
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Detailed Explanation
The proportion (1/2) mile/4minutes = x miles /15minutes models this situation.
Cross multiply \(\frac{\mathrm{1} }{\mathrm{2}}\) × 15 = 4x, so \(\frac{\mathrm{15} }{\mathrm{2}}\) = 4x and x = \(\frac{\mathrm{15} }{\mathrm{2}}\) × \(\frac{\mathrm{1} }{\mathrm{4}}\) =\(\frac{\mathrm{15} }{\mathrm{8}}\)=\(1\frac{\mathrm{7} }{\mathrm{8}}\)) miles.
Cross multiply \(\frac{\mathrm{1} }{\mathrm{2}}\) × 15 = 4x, so \(\frac{\mathrm{15} }{\mathrm{2}}\) = 4x and x = \(\frac{\mathrm{15} }{\mathrm{2}}\) × \(\frac{\mathrm{1} }{\mathrm{4}}\) =\(\frac{\mathrm{15} }{\mathrm{8}}\)=\(1\frac{\mathrm{7} }{\mathrm{8}}\)) miles.
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