A school trip covered 1/3rd of the journey by boat, 2/5th by train by bus and remaining distance of 7200m by foot. What is the difference between the distance covered by train and bus
Answers
Answer:
Let total journey is x .
So,
Journey covered by boat = \frac{1}{3} *x
3
1
∗x
Journey covered by train = \frac{2}{5} *x
5
2
∗x
Journey covered by bus = \frac{1}{15} *x
15
1
∗x
Remaining journey by foot = 7200 M
So
total journey = Journey by (boat + train + bus + foot)
\begin{gathered}x = \frac{1}{3} *x + \frac{2}{5} *x + \frac{1}{15} *x + 7200\\x = \frac{x}{3} + \frac{2x}{5} + \frac{x}{15} + 7200\\\\\end{gathered}
x=
3
1
∗x+
5
2
∗x+
15
1
∗x+7200
x=
3
x
+
5
2x
+
15
x
+7200
LCM of R.H.S
\begin{gathered}x = \frac{5x+6x+x+108000}{15} \\15x=12x + 108000\\15x-12x=108000\\x = \frac{108000}{3} \\x=36000 Meters\end{gathered}
x=
15
5x+6x+x+108000
15x=12x+108000
15x−12x=108000
x=
3
108000
x=36000Meters
Total Distance = x = 36000 Meters.
Difference = Distance cover by train - bus
= \begin{gathered}\frac{2}{5} *36000 - \frac{1}{15} *36000\\2* 7200 - 2400\\14400-2400\\12000 Meters\end{gathered}
5
2
∗36000−
15
1
∗36000
2∗7200−2400
14400−2400
12000Meters