Question

Jagan went to another town such that he covered \[240{\text{ km}}\] by a car going at \[60{\text{ km }}{{\text{h}}^{ - 1}}\]. Then he covered \[80{\text{ km}}\] by a train, going at \[100{\text{ km }}{{\text{h}}^{ - 1}}\] and the rest \[200{\text{ km}}\], he covered by a bus, going at \[50{\text{ km }}{{\text{h}}^{ - 1}}\]. What was his average speed during the whole journey?

Answer 1

Hint: The given problem is based on the time and distance. In this question we are going to find the average speed of Jagan during his whole journey using the formulas listed here.​ To solve this problem we must know the relationship between the distance (\[d\]), speed (\[s\]) and time (\[t\]). The relationship can be explained through the formula, \[d = s \times t\].

Complete step-by-step answer:
We are given that Jagan travels by car, train and bus to cover the distances \[240{\text{ km}}\], \[80{\text{ km}}\] and \[200{\text{ km}}\] in the speed of \[60{\text{ km per hour}}\], \[100{\text{ km per hour}}\] and \[50{\text{ km per hour}}\].
We need to find the average speed, let find the formula of speed by the distance formula: \[d = s \times t\].
By converting this formula in terms of speed we will get, \[s = \dfrac{d}{t}\], this is the formula for finding speed. In our question we are asked to find the average then the formula will be altered slightly,
 \[{\text{Average(s)}} = \dfrac{{{\text{Total distance}}}}{{{\text{Total time}}}}\].
We can calculate the distance as follows:
\[{\text{Total distance}} = {d_1} + {d_2} + {d_3}\]
\[ = 240 + 80 + 200\]
\[ = 520\]
Total distance \[ = 520{\text{ km}}\].
\[{\text{Total time}} = {t_1} + {t_2} + {t_3}\].
In our question time taken by Jagan to cover each distance is not given. So let's find the time.
Since we know the speed formula, \[s = \dfrac{d}{t}\]. Let's find \[t\] from this.
By cross multiplying \[s\] and \[\operatorname{t} \], we will get \[t = \dfrac{d}{s}\].
Time taken by Jagan to cover the \[240{\text{ km}}\] at the speed of \[60{\text{ km per hour}}\],\[{t_1} = \dfrac{{{d_1}}}{{{s_1}}}\]
\[{t_1} = \dfrac{{240}}{{60}}\]
By cancelling zeroes, we will get,
\[ = \dfrac{{24}}{6}\]
By dividing \[24\] by \[6\], we will get \[4\], because \[6 \times 4 = 24\].
\[{t_1} = 4\].
S.I unit of time is hour ( \[{\text{h}}\]). In our question also the data are in hour format.
Therefore, \[4\] hours is taken by Jagan to cover the \[240{\text{ km}}\] at the speed of \[60{\text{ km per hour}}\], \[{t_1} = 4{\text{ hrs}}\].
Time taken by Jagan to cover the \[80{\text{ km}}\] at the speed of \[100{\text{ km per hour}}\], \[{t_2} = \dfrac{{{d_2}}}{{{s_2}}}\].
\[{t_2} = \dfrac{{80}}{{100}}\]
By cancelling zeroes we will get,
\[ = \dfrac{8}{{10}}\]
Cancelling both numerators and denominators by \[2\],
\[ = \dfrac{4}{5}\]
By further division we will get,
\[{t_2} = 0.8\]
\[0.8\] hours is taken by Jagan to cover the \[80{\text{ km}}\] at the speed of \[100{\text{ km per hour}}\], \[{t_2} = 0.8{\text{ hrs}}\].
Time taken by Jagan to cover the \[200{\text{ km}}\] at the speed of \[50{\text{ km per hour}}\], \[{t_3} = \dfrac{{{d_3}}}{{{s_3}}}\]
\[{t_3} = \dfrac{{200}}{{50}}\]
Cancel the zeroes
\[ = \dfrac{{20}}{5}\]
Dividing both by \[5\],
\[{t_3} = 4\]
\[4\] hours is taken by Jagan to cover the \[200{\text{ km}}\] at the speed of \[50{\text{ km per hour}}\], \[{t_3} = 4{\text{ hrs}}\].
Now by using, \[{\text{Total time}} = {t_1} + {t_2} + {t_3}\]
\[ = 4 + 0.8 + 4\]
\[ = 8.8\]
\[{\text{total time}} = 8.8{\text{ hrs}}\].
Now, we have to calculate the average speed by the formula ,
\[s = \dfrac{{{\text{total distance}}}}{{{\text{total time}}}}\]
\[ = \dfrac{{520}}{{8.8}}\]
\[ = 59.09\]
The S.I unit of speed is \[{\text{km}}\]per hour and our question also follows the same.
Therefore, the average speed taken by Jagan is \[{\text{59}}{\text{.09 km per hour}}\].
So, the correct answer is “\[{\text{59}}{\text{.09 km per hour}}\]”.

Note: One should read the question to understand the given and be aware of the units used in the question to represent distance, speed and time. All the units in the problem should be the same. If it is not the same we can convert it to make it the same. It is very important because if the units are not the same then the answer we get will be wrong.