Question

When building the Channel, the English and French each started drilling on opposite sides of the English Channel. The two sections became one in 1990. The French used more advanced drilling machinery than the English. Suppose the English could drill the Channel in 6.2 years, and the French could drill in 5.8 years, how long would it have taken the two together?

Answer 1

Suppose the English could drill the Channel in 6.2 years, then they drill with speed $\dfrac{L}{6.2}$ 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 $\dfrac{L}{5.8}$ km per year.

Together their speed will be

$\dfrac{L}{6.2} +\dfrac{L}{5.8} =\dfrac{5.8L+6.2L}{6.2\cdot 5.8}=\dfrac{12L}{35.96}=\dfrac{3L}{8.99}$.

If they drill together, they will spend

$\dfrac{L}{\frac{3L}{8.99}} =\dfrac{8.99}{3}=2.9966666....\approx 3$ years.

Answer: it would have taken nearly 3 years.