Formulate the following problems as a part of equations, and hence find their solutions.
(i) 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.
Solution:
Let speed of rowing in still water
km/h
Let speed of current
km/h
So, speed of rowing downstream
km/h
And, speed of rowing upstream
km/h
According to given conditions, we have
and
and
(1) and
(2)
Adding (1) and (2), we get
Putting
in (1), we get
Therefore, speed of rowing in still water
km/h
Speed of current
km/h
(ii) 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 1 woman alone to finish the work, and also that taken by 1 man alone.
Solution:
Let time taken by 1 woman alone to finish the work
days
Let time taken by 1 man alone to finish the work
days
So, 1 woman’s 1 day work
part of the work
And, 1 man’s 1 day work
part of the work
So, 2 women’s 1 day work
part of the work
And, 5 men’s 1 day work
part of the work
Therefore, 2 women and 5 men’s 1 day work
part of the work (1)
It is given that 2 women and 5 men complete work in = 4 days
It means that in 1 day, they will be completing
part of the work. (2)
Clearly, we can see that (1) = (2)
(3)
Similarly, 3 women’s 1 day work
part of the work
And, 6 men’s 1 day work
part of the work
Therefore, 3 women and 6 men’s 1 day work
part of the work (4)
It is given that 3 women and 6 men complete work in = 3 days
It means that in 1 day, they will be completing
part of the work. (5)
Clearly, we can see that (4) = (5)
(6)
Let
and
Putting this in (3) and (6), we get
and
(7) and
(8)
Multiplying (7) by 9 and (8) by 8, we get
(9)
(10)
Substracting (10) from (9), we get
Putting this in (8), we get
Putting values of p and q in
and
, we get
and
Therefore, 1 woman completes work in
days
And, 1 man completes work in
days
(iii) Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.
Solution:
Let speed of train
km/h
Let speed of bus
km/h
According to given condition, we have
and
Let
and
Putting this in the above equations, we get
(1) and
(2)
Multiplying (1) by 5 and (2) by 3 we get
(4)
(5)
Subtracting (5) from (4), we get
Putting value of q in (2), we get
We know that
and
Therefore,
km/h and
km/h
Therefore, speed of train
km/h
And, speed of bus
km/h
aradhya rathore says
THANKYOUUU……
It was really helpful to me
Naren. S says
Very good and a perfect solution