Question

A person divides his total journey into three equal parts and decides to travel the three parts with the speeds of 40, x and 15 km/h, respectively. If his average speed during the whole journey is 24 km/h, then find the value of x.

• A. 30 km/h
• B. 38 km/h
• C. 32 km/h
• D. 35 km/h

Answer 1

Answer:

A. 30 km/h

Solution:

Given:

A person divides his journey into three equal parts and travels three parts with speeds of 40 km/h, X km/h, and 15 km/h

Average speed for the whole journey = 24 km/h

Formula Used:

Average Speed $=\frac{D1+D2+D3+....+Dn}{\frac{D1}{S1}+\frac{D2}{S2}+\frac{D3}{S3}+....+\frac{Dn}{Sn}}$

Where D1, D2, D3, Dn are distances and S1, S2, S3, Sn are respective speeds

Calculation:

Let the total distance of the journey be 360 km (120 + 120 + 120)

According to the question

$24=\frac{120+120+120}{\frac{120}{40}+\frac{120}{x}+\frac{120}{15}}$

$24=\frac{360}{3+8+\frac{120}{x}}$

$24=\frac{360}{11+\frac{120}{x}}$

$264+\frac{24\times 120}{x}=360$

$264(1+\frac{24\times 120}{x})=360$

$\frac{24\times 120}{x}=96$

$x=\frac{24\times 120}{96}=30km/h$

The value of x is 30 km/h.