Question

manoj travelled one third of a distance at an average speed of 16 km/hr then half of distance at a speed of 15Km/hr and covered the rest of distance at an average speed of 20km/hr.If he took total of 15 hours in completing the journey then total distance covered by him is​

Answer 1

Given,

$\[\frac{1}{3}\]$ of distance covered with an average speed of $\[16km/hr\]$.

half of distance at a speed of $\[15km/hr\]$.

Rest of the distance covered with $\[20km/hr\]$.

Total time required for journey $\[ = 15hours\]$

Solution,

Consider the total distance is x km.

$\[\frac{x}{{3 \times 16}} + \frac{{2x}}{{3 \times 2 \times 15}} + \frac{{2x}}{{3 \times 2 \times 20}} = 15\]$

$\[ \Rightarrow \frac{x}{{3 \times 16}} + \frac{x}{{3 \times 15}} + \frac{x}{{3 \times 20}} = 15\]$

$\[ \Rightarrow \frac{x}{3}\left( {\frac{1}{{16}} + \frac{1}{{15}} + \frac{1}{{20}}} \right) = 15\]$

$\[ \Rightarrow \frac{x}{3}\left( {\frac{1}{{16}} + \frac{{4 + 3}}{{60}}} \right) = 15\]$

$\[ \Rightarrow \frac{x}{3}\left( {\frac{1}{{16}} + \frac{7}{{60}}} \right) = 15\]$

$\[ \Rightarrow \frac{x}{3}\left( {\frac{{15 + 4}}{{240}}} \right) = 15\]$

$\[ \Rightarrow x \times \frac{{19}}{{240}} = 45\]$

$\[ \Rightarrow x = 568.42km\]$

Hence the total distance covered by Manoj in journey is $\[568.42km\]$

Answer 2

Answer:

Let's take total distance travelled in parts are 6

We have to find here Average Speed = Total distance travelled / Total time taken

Total distance travelled in parts are 6

Total time taken = distance_1/speed_1 + ....

1st one is 1/3rd of distance which is 1/3rd of 6 = 2 at speed of 16km/h

2nd one is 1/2 of distance which is 1/2 of 6 = 3 at speed of 15km/h

Average Speed = 6/ (2/16 + 3/15 + 1/20)

= (6/15)*40

We have Average Speed now & total time also A.T.Q = 15 hours

So Total distance = Average Speed * Total time

= (6/15)*40 * 15

= 6*40*15/15

= 6*40

= 240 Km

Ans = 240 Km