Question

A car covers four successive 8 km distances at speeds of 12 km/hr, 18 km/hr, 24 km/hr and 36 km/hr, respectively. Its average speed (in km/hr) over this distance is:

• A. 19.2
• B. 20
• C. 18
• D. 22.5

Answer 1

Answer:

A. 19.2

Each segment is 8 km, so total distance = ( 4 \times 8 = 32 ) km.

Time taken for each segment:

$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

• At 12 km/hr: $( \frac{8}{12} = \frac{2}{3} ) hr$

• At 18 km/hr: $( \frac{8}{18} = \frac{4}{9} ) hr$

• At 24 km/hr: $( \frac{8}{24} = \frac{1}{3} ) hr$

• At 36 km/hr: $( \frac{8}{36} = \frac{2}{9} ) hr$

  Total time:

$\frac{2}{3} + \frac{4}{9} + \frac{1}{3} + \frac{2}{9}$

Convert to common denominator (9):
$\frac{6}{9} + \frac{4}{9} + \frac{3}{9} + \frac{2}{9} = \frac{15}{9} = \frac{5}{3} \text{ hr}$

Average Speed:

$\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{32}{5/3} = 32 \times \frac{3}{5} = 19.2 \text{ km/hr}$

Average speed = 19.2 km/hr