Question

A bus covers 10 miles at an average speed of 60 mi/h. If it covers the first 3 miles at 60 mi/h and the next 5 miles at 50 mi/h, at what speed does it cover the remaining 2 miles?

• A. 60 mi/h
• B. 80 mi/h
• C. 100 mi/h
• D. 120 mi/h

Answer 1

The correct option is D 120 mi/h

Examining each stretch of the journey, we find:

$StretchA:\text{Distance}=3miles;\text{Speed}=60mi/h$

$\text{Time taken to cover stretch A}=\frac{Distance}{Speed}=\frac{3}{60}=\frac{1}{20}hours$

$StretchB:\text{Distance}=5miles;\text{Speed}=50mi/h$

$\text{Time taken to cover stretch A}=\frac{Distance}{Speed}=\frac{5}{50}=\frac{1}{10}hours$

$StretchC:\text{Distance}=2miles;\text{Speed}{=}^{\prime }{S}^{\prime }mi/h$

$\text{Time taken to cover stretch A}=\frac{Distance}{Speed}=\frac{2}{S}hours$

$Averagespeed=\frac{Totaldistance}{Totaltime}$

$⟹60mi/h=\frac{10miles}{\frac{1}{20}+\frac{1}{10}+\frac{2}{S}}$

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

$\frac{60}{20}mi+\frac{60}{10}mi+\frac{120}{S}mi=10mi$

$⟹3+6+\frac{120}{S}=10$

$⟹\frac{120}{S}=10–9=1$

$⟹S=120mi/h$