Question

A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 8 km/hr, respectively, and takes a total of 425 minutes. What is the total distance (in km) travelled?

• A. 32
• B. 28
• C. 27
• D. 30

Answer 1

Answer:

D. 30

Let the equal distance for each part be (d) km.

Time taken for each part

$\frac{d}{3}, \quad \frac{d}{4}, \quad \frac{d}{8}$

Total time

$\frac{d}{3} + \frac{d}{4} + \frac{d}{8} = 425 \text{ minutes} = \frac{425}{60} = \frac{85}{12} \text{ hours}$

Add fractions

$\frac{d}{3} + \frac{d}{4} + \frac{d}{8}$

$= \frac{8d + 6d + 3d}{24}$

$= \frac{17d}{24}$

So,
$\frac{17d}{24} = \frac{85}{12}$

Solve

$17d = \frac{85}{12} \times 24 = 170$

$d = \frac{170}{17} = 10$

Total distance

$3d = 3 \times 10 = 30 \text{ km}$

Total distance = 30 km