Manoj travels one third of a distance at an average speed of 16 law, then half of the distance at a speed of 15 kmh and covered the
Answers
Explanation:
Given,
\frac{1}{3}
3
1
of distance covered with an average speed of 16km/hr16km/hr .
half of distance at a speed of 15km/hr15km/hr .
Rest of the distance covered with 20km/hr20km/hr .
Total time required for journey = 15hours=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
3×16
x
+
3×2×15
2x
+
3×2×20
2x
=15
\Rightarrow \frac{x}{{3 \times 16}} + \frac{x}{{3 \times 15}} + \frac{x}{{3 \times 20}} = 15⇒
3×16
x
+
3×15
x
+
3×20
x
=15
\Rightarrow \frac{x}{3}\left( {\frac{1}{{16}} + \frac{1}{{15}} + \frac{1}{{20}}} \right) = 15⇒
3
x
(
16
1
+
15
1
+
20
1
)=15
\Rightarrow \frac{x}{3}\left( {\frac{1}{{16}} + \frac{{4 + 3}}{{60}}} \right) = 15⇒
3
x
(
16
1
+
60
4+3
)=15
\Rightarrow \frac{x}{3}\left( {\frac{1}{{16}} + \frac{7}{{60}}} \right) = 15⇒
3
x
(
16
1
+
60
7
)=15
\Rightarrow \frac{x}{3}\left( {\frac{{15 + 4}}{{240}}} \right) = 15⇒
3
x
(
240
15+4
)=15
\Rightarrow x \times \frac{{19}}{{240}} = 45⇒x×
240
19
=45
\Rightarrow x = 568.42km⇒x=568.42km
Hence the total distance covered by Manoj in journey is 568.42km568.42km