2. Formulate the following problems as a pair of equations, and hence find their solutions
(1) Ritu can row downstream 20 km in 2 hours and upstream 4 km in 2 hours Find her
speed of rowing in still water and the speed of the current
(2) 2 women and 5 men can together finish an embroidery work in 4 days, while 3
women and 6 men can finish it in 3 days. Find the time taken by I woman alone to
finish the work, and also that taken by 1 man alone.
(3) Roohi travels 300 km to her home partly by train and partiy by bus She takes 4
hours if she travels 60 km by train and the remaining by bus If she travels 100 kan
by train and the remaining by bus, she takes 10 minutes longer. Find the speed of
the train and the bus separately.
I need all answer with complete solution .
Answers
Step-by-step explanation:
Let, speed of Ritu in still water be x km/hr
and speed of current be y km/hr
Then speed downstream =(x+y) km/hr
speed upstream =(x−y) km/hr
we know, Time=
Speed
Distance
Then
x+y
20
=2 and
x−y
4
=2
⇒x+y=10 ...(1)
& x−y=2 ...(2)
adding both we get, 2x=12⇒x=6
Thus using (1) y=10−6=4
Hence the speed of Ritu in still water is 6 km/hr and the speed of the current is 4 km/hr.
2. Let the work done by man and woman per day be x and y respectively.
When the work is completed in 4 days
Since 5 men and 2 women complete the work in 4 days
therefore work done by 5 men and 2 women in 1 day =
4
1
∴5x+2y=
4
1
⟶eq
n
1
When the work is completed in 3 days
Since 6 men and 3 women complete the work in 3 days
therefore work done by 6 men and 3 women in 1 day =
3
1
∴6x+3y=
3
1
⟶eq
n
2
Multiplying by 3 in eq
n
1, we get
⇒15x+6y=
4
3
⟶eq
n
3
Multiplying by 2 in eq
n
2, we get
⇒12x+6y=
3
2
⟶eq
n
4
On subtracting eq
n
4 from eq
n
3, we get
⇒15x+6y−12x−6y=
4
3
−
3
2
⇒3x=
12
1
⇒x=
36
1
On substituting the value of x in eq
n
2, we get
⇒6×
36
1
+3y=
3
1
⇒3y=
3
1
−
6
1
⇒y=
18
1
Thus,
work done by 1 man in 1 day =
36
1
days
∴ Time taken by 1 man alone to finish the work =36 days
work done by 1 woman in 1 day =
18
1
days
∴ Time taken by 1 woman alone to finish the work =18 days
3.
Let the speed of the train be x km/hr and the speed of the bus is y km/hr.
So according to question and using Time=
Speed
Distance
Total distance =300 km
Roohi travels 60 km by train and 300−60=240 by bus in 4 minute,
x
60
+
y
240
=4
and 100 km by train, 300−100=200 by bus, and takes 10 minutes more,
x
100
+
y
200
=4+
60
10
⇒
x
100
+
y
200
=
6
25
Now, let
x
1
=u and
y
1
=v
then 60u+240v=4.............eq1
100u+200v=
6
25
..............eq2
multiply eq1 by 5 and eq2 by 6 we get
300u+1200v=20..........eq3
600u+1200v=25...........eq4
Subtracting eq3 qnd eq4 we get
−300u=−5
u=
300
5
=
60
1
Putting the value of u in eq1 we get
60×
60
1
+240v=4
240v=3
v=
240
3
=
80
1
Now
x
1
=u=
60
1
∴x=60
and
y
1
=v=
80
1
∴y=80
Hence the speed of the train is 60 km/hr and the speed of the bus is 80 km/hr.
Answer:
i think the above ones answer is correct