A man travels 500 km partly by train and partly by bus. He takes 5 hours 30 minutes
if he travels 300 km by train and the rest by bus. If he travels 260 km by train and
240 km by bus, he takes 6 minutes longer. Find the speed of the train and the bus separately..... Pls help
Answers
Answer:
"takes"
Step-by-step explanation:
Let, the speed of train be x & speed of bus be y.
Speed=
Time
Distance
or T=
S
D
4=
x
60
+
y
240
………….(1)
4 hr 10 min=
x
100
+
y
200
………..(2)
(1)×5
20=
x
300
+
y
240×S
(2)×3
62
25×3
=
x
300
+
y
600
20−
2
25
=
y
1200
−
y
600
2
15
=
y
600
y=80 km/ph
4=
x
60
80+240
x=60 km/ph.
Step-by-step explanation:
Let, the speed of train be x & speed of bus be y.
T = d
-----
s
5.5 hour = 300/x + 200/y ........ (1)
5.6 hour = 260/x + 240/y .......... (2)
260-300/x + 240-200/y = 5.6-5.5 => 0.1 hr
-40/ x + 40/y = 0.1 hr
-40[ 1/x - 1/y] = 0.1 hr
1/x - 1/y = -0.1/40
1/x - 1/y = -0.1 × 10 /40 × 10 => -1/400
y-x/xy = -1/400
400(y-x)= -xy
400(y - x) + xy = 0
400 y - 400 x + xy = 0
400 y + xy = 400 x
y( 400+ x) = 400 x
y= (400 x/ 400+ x)
300/x + 200/y = 5.5×10/10 => 55/10
300/x + 200( 400+ x)/400x = 55/10
300/x + 400+x/2x = 55/10
600+400+x/2x = 55/10
10(1000) +10x = 55× 2x
10× 1000+10x = 110x
110x - 10 x= 10× 1000
100x = 10000
x= 100 km / hr
y = 400x/400+ x
y= 400× 100/400+100
y = 40000/500