A man travelled 120 km to a town. he could have reached the town 4.5 hours earlier had increased his speed by 3km/h. Find the speed at which he traveled?
Answers
Answer:
Length of the journey = 50 km, uniform speed of the man = 8 km/hr
Let length of the journey be
x
km,
uniform speed of the man be
s
km/hr
If speed of man had been 2 km/h faster ,it would have taken 1 hour 15 minutes less than the scheduled time.
1 hour 15 minutes =
1
15
60
hour =
1
1
4
hour =
5
4
hour
From the above, we have
x
s
+
2
=
x
s
−
5
4
x
s
−
x
s
+
2
=
5
4
(
s
+
2
)
x
−
s
x
s
(
s
+
2
)
=
5
4
2
x
s
(
s
+
2
)
=
5
4
⋯
(
1
)
If speed of the man were slower by 2 km/h, the man would have taken, 2 hour 5 minutes more than the scheduled time
2 hour 5 minutes =
2
5
60
hour =
2
1
12
hour =
25
12
hour
From the above, we have
x
s
−
2
=
x
s
+
25
12
x
s
−
2
−
x
s
=
25
12
s
x
−
(
s
−
2
)
x
s
(
s
−
2
)
=
25
12
2
x
s
(
s
−
2
)
=
25
12
⋯
(
2
)
We have two equations and two variables. Solve them for x and s
(1)/(2)=>
s
−
2
s
+
2
=
5
×
12
4
×
25
s
−
2
s
+
2
=
3
5
5
s
−
10
=
3
s
+
6
2
s
=
16
s
=
8
From(1),
2
x
s
(
s
+
2
)
=
5
4
2
x
8
(
8
+
2
)
=
5
4
x
=
50
Step-by-step explanation: