Suppose the English could drill the Channel in 6.2 years, then they drill with speed [tex] \dfrac{L}{6.2} [/tex] km per year, where L is the length of the English Channel. If the French could drill in 5.8 years, then their speed of drillling is [tex] \dfrac{L}{5.8} [/tex] km per year.
Together their speed will be
[tex] \dfrac{L}{6.2} +\dfrac{L}{5.8} =\dfrac{5.8L+6.2L}{6.2\cdot 5.8}=\dfrac{12L}{35.96}=\dfrac{3L}{8.99} [/tex].
If they drill together, they will spend
[tex] \dfrac{L}{\frac{3L}{8.99}} =\dfrac{8.99}{3}=2.9966666....\approx 3 [/tex] years.
Answer: it would have taken nearly 3 years.
