Work

The first paving machine can pave a pavement in 28 hours, and the second in 26 hours. The first machine started working, and after 2 hours the second machine joined it. How long after the second machine starts will they finish the job together?

Final Answer:

x =  14.5 h

Step-by-step explanation:

$$\begin{gathered} a=28\text{h} \\ b=26\text{h} \\ A=\frac{1}{a}=\frac{1}{28}\doteq 0.03571\text{/h} \\ B=\frac{1}{b}=\frac{1}{26}\doteq 0.03851\text{/h} \\ s=A+B=0.0357+0.0385=\frac{27}{364}\doteq 0.07421\text{/h} \\ 2\cdot A+(x-2)\cdot s=1 \\ 2\cdot 0.035714285714286+(x-2)\cdot 0.074175824175824=1 \\ 0.074176x=1.076923 \\ x=\frac{1.07692308}{0.07417582}=14.51851852 \\ x=\frac{392}{27}\doteq 14.518519=14.5\text{h} \end{gathered}$$

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