Question

A person can complete a journey in 9 hours. He covers the first one-third part of the journey at the rate of 35 km/h and the remaining distance at the rate of 28 km/h. What is the total distance (in km) of his journey?

• A. 268
• B. 275
• C. 270
• D. 277

Answer 1

Answer:

C. 270

The total distance of the journey is 270 km.

1. Define the Variables

   • Let the total distance be $D$.

   • First part of the distance = $\frac{D}{3}$

   • Remaining part of the distance = $\frac{2D}{3}$

2. Set up the Time Equation

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

   • Time for first part ($t_1$) = $\frac{D / 3}{35} = \frac{D}{105}$ hours

   • Time for second part ($t_2$) = $\frac{2D / 3}{28} = \frac{D}{42}$ hours

3. Solve for $D$

   • Total time = $t_1 + t_2 = 9$ hours

   • $\frac{D}{105} + \frac{D}{42} = 9$

   • Find a common denominator for 105 and 42, which is 210:
     $\frac{2D + 5D}{210} = 9$
     $\frac{7D}{210} = 9$
     $\frac{D}{30} = 9$
     $D = 270\text{ km}$