Question

One third of a certain journey is covered at the rate of 25 km/hr. one 1fourth at the rate of 30 km/hr. and the rest at 50 km/hr. The average speed for the whole journey is?​

Answer 1

ANSWER:-

Given:

One third of a certain journey is covered at the rate of 25km/hr. One-fourth at the rate of 30 km/hr. & the rest at 50km/hr.

To find:

The average speed for the whole journey.

Solution:

Let the total distance covered for journey be x km.

$= > {}^{T} 1 = \frac{ \frac{x}{3} }{25} \\ \\ = > \frac{x}{75}hrs. \\ \\ = > {}^{t} 2 = \frac{ \frac{x}{4} }{30} \\ \\ = > \frac{x}{120} hrs.$

Rest distance:

$= > x - ( \frac{x}{3} + \frac{x}{4} ) \\ \\ = > x - ( \frac{4x + 3x}{12} ) \\ \\ = > x - \frac{7x}{12} \\ \\ = > \frac{12x - 7x}{12} \\ \\ = > \frac{5x}{12} km$

${}^{T} 3 = \frac{ \frac{5x}{12} }{50} \\ \\ = > \frac{5x}{12 \times 50} \\ \\ = > \frac{x}{120} hrs.$

Now,

Total distance= x km.

Total time:

$= > {}^{</u><u>T</u><u>} 1 + {}^{</u><u>T</u><u>} 2 + {}^{</u><u>T</u><u>} 3 \\ \\ = > \frac{x}{75} + \frac{x}{120} + \frac{x}{120} \\ \\ = > \frac{8x + 5x + 5x}{600} \\ \\ = > \frac{18x}{600} \\ \\ = > \frac{3x}{100} hrs.$

Average Speed:

$= > \frac{Total \:distance}{Total \: time} \\ \\ = > \frac{x}{ \frac{3x}{100} } \\ \\ = > 33.33km/hr.$

Hope it helps ☺️