A teacher 2

A teacher checked two sets of test papers. The first set took 3 3/4 hours. The second took 1 1/2 hours, and the third took 2 3/5 hours. How much faster did the teacher check the third set than the first and second?

Correct answer:

r₁ =  1 ²³⁄₅₂ = 75/52
r₂ =  15/26

Step-by-step explanation:

$$\begin{gathered} a=3\frac{3}{4}=3+\frac{3}{4}=\frac{3\cdot 4+3}{4}=\frac{12+3}{4}=\frac{15}{4}=3\frac{3}{4}=3.75 \\ b=1\frac{1}{2}=1+\frac{1}{2}=\frac{1\cdot 2+1}{2}=\frac{2+1}{2}=\frac{3}{2}=1\frac{1}{2}=1.5 \\ c=2\frac{3}{5}=2+\frac{3}{5}=\frac{2\cdot 5+3}{5}=\frac{10+3}{5}=\frac{13}{5}=2\frac{3}{5}=2.6 \\ {r}_1=a/c=\frac{15}{4}/\frac{13}{5}=\frac{15}{4}:\frac{13}{5}=\frac{15}{4}\cdot \frac{5}{13}=\frac{15\cdot 5}{4\cdot 13}=\frac{75}{52}=1\frac{23}{52}=1.4423 \end{gathered}$$

$r_2=b/c=\frac{3}{2}/\frac{13}{5}=\frac{3}{2}:\frac{13}{5}=\frac{3}{2}\cdot \frac{5}{13}=\frac{3\cdot 5}{2\cdot 13}=\frac{15}{26}=0.5769$

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