Question

A motor bike covers 10 miles at an average speed of 60 mph. If it covers the first 3 miles at 60 mph and the next 5 miles at 50 mph, at what speed does it cover the remaining 2 miles?

Answer 1

Examining each part of the journey, we find:

\(Part\ 1: \\ \text{Distance} = 3\ miles;\ \text{Speed} = 60\ mph\)

\(\text{Time taken to cover part 1}\\ = \dfrac{Distance}{Speed} = \dfrac{3}{60} = \dfrac{1}{20}\ hours\)

\(Part\ 2: \\ \text{Distance} = 5\ miles;\ \text{Speed} = 50\ mph\)

\(\text{Time taken to cover part 2}\\ = \dfrac{Distance}{Speed} = \dfrac{5}{50} = \dfrac{1}{10}\ hours\)

\(Part\ 3: \\ \text{Distance} = 2\ miles;\ \text{Speed} = 'S'\ mph\)

\(\text{Time taken to cover part 3}\\ = \dfrac{Distance}{Speed} = \dfrac{2}{S}\ hours\)

\(Average\ speed = \dfrac{Total\ distance}{Total\ time}\)

\(\implies 60\ mph = \dfrac{10\ miles}{\dfrac{1}{20} + \dfrac{1}{10} + \dfrac{2}{S}}\)

Multiplying both sides of the equation with the denominator, we get:

\(\dfrac{60}{20}\ + \dfrac{60}{10}\ + \dfrac{120}{S}\ = 10\ miles\)

\(\implies 3 + 6 + \dfrac{120}{S} = 10\)

\(\implies \dfrac{120}{S} = 10 – 9 = 1\)

\(\implies S = 120\ mph\)