1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
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?

Open in App
Solution

## 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: $$\dfrac{60}{20}\ + \dfrac{60}{10}\ + \dfrac{120}{S}\ = 10\ miles$$ $$\implies 3 + 6 + \dfrac{120}{S} = 10$$ $$\implies \dfrac{120}{S} = 10 – 9 = 1$$ $$\implies S = 120\ mph$$

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Basics of Data
MATHEMATICS
Watch in App
Join BYJU'S Learning Program