Question

The total distance between two stations is 570 km out of which, 224 km is covered at 56 km/hr, 210 km is covered at 70 km/hr and the remaining is covered in 2 hours. Find the average speed during the whole journey.
(a) $14\dfrac{1}{3}\text{ km/hr}$
(b) $52\dfrac{1}{3}\text{km/hr}$
(c) $75\dfrac{1}{3}\text{km/hr}$
(d) $63\dfrac{1}{3}\text{km/hr}$

Answer 1

Hint: To find the average speed during the whole journey, we have to find the time taken to cover each of the given distance using the formula $\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}$ . We will denote time taken to cover 224 km as ${{T}_{1}}$ , that for 210 km as ${{T}_{2}}$ and the given time 2 hr as ${{T}_{3}}$ . then, the average speed will be the total traveled distance divided by the total time ( i.e., sum of ${{T}_{1}}$ , ${{T}_{2}}$ and ${{T}_{3}}$ ).

Complete step by step solution:
We have to find the average speed during the whole journey. We are given that 224 km is covered at 56 km/hr. Let us find the time taken to cover 224 km. Let us denote this time as ${{T}_{1}}$ .
We know that $\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}$
From the above formula, we will get
$\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}$
$\Rightarrow {{T}_{1}}=\dfrac{224}{56}=4\text{ hr}$
We are also given that 210 km is covered at 70 km/hr. We have to find the time taken for this, Let us denote this time as ${{T}_{2}}$ .
$\Rightarrow {{T}_{2}}=\dfrac{210}{70}=3\text{ hr}$
We are given that the remaining distance is covered in 2 hr. Let us denote ${{T}_{3}}=2\text{ hr}$ .
We know that $\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}$
Therefore, $\text{Average Speed}=\dfrac{\text{Total Distance Travelled}}{\text{Total Time Taken}}$
We are given that total distance travelled = 570 km.
We can find the total time taken by adding ${{T}_{1}}$ , ${{T}_{2}}$ and ${{T}_{3}}$ .
$\Rightarrow \text{Total time taken}={{T}_{1}}+{{T}_{2}}+{{T}_{3}}=4+3+2=9\text{ hr}$
Therefore, $\text{Average Speed}=\dfrac{570}{9}=63\dfrac{1}{3}\text{ km}/\text{hr}$
Hence, the correct option is d.

Note: Students have the chance of making mistakes when writing the formula for speed as $\text{Speed}=\text{Distance}\times \text{Time}$ and thus making mistakes in the average speed formula. They must never miss out the units. The final answer must be in whole fraction since the options are in whole fraction.