Abdul travelled 300 km by train and 200 km by taxi taking 5 hours 30 minutes. But, of he travels 260 km by train and 240 by taxi, he takes 6 minutes longer. Find the speed of the train and that of the tax i.
Answers
Let the speed of train be x km/hr and speed of taxi be y km/hr.
We know, Time=
Speed
Distance
5 hr 30 minutes =5+
60
30
=5+
2
1
=
2
11
hrs
5 hr 36 minutes =5+
60
36
=5+
10
6
=
5
28
hrs
From the given information, we have,
x
300
+
y
200
=
2
11
and
x
260
+
y
240
=
5
28
Putting
x
1
=pand
y
1
=q , we have
300p+200q=
2
11
and260p+240q=
5
28
or,300p+200q=
2
11
⇒100(3p+2q)=
2
11
⇒2(3p+2q)=0.11
⇒6p+4q=0.11....(i)
Also,260p+240q=
5
28
⇒20(13p+12q)=
5
28
⇒13p+12q=0.28
⇒12q=0.28−13p
⇒q=
12
0.28−13p
....(ii)
Substituting equation (ii) in equation (i), we get,
6p+4q=0.11
⇒6p+4(
12
0.28−13p
)=0.11
⇒6p+
3
0.28
−
3
13p
=0.11
⇒
3
5p
=0.11−
3
0.28
⇒5p=0.33−0.28
⇒p=
5
0.05
=
100
1
Substituting p=
100
1
in equation (ii), we get,
q=
12
0.28−13p
=
12
0.28−13×
100
1
=
12
0.28−0.13
=
12
0.15
=
80
1
p=
x
1
=
100
1
⇒x=100
q=
y
1
=
80
1
⇒y=80
Thus, speed of train =x=100 km/hr and speed of taxi =y=80 km/hr.
Answer:
4689/8-8-97=^578
Explanation: