Formulate the following problems as a pair of equation and then find their solution.
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 and 1 man alone to finish the work.

Question

Formulate the following problems as a pair of equation and then find their solution.
Rahim travels 600 km to his home partly by train and partly by car. He takes 8 hours if he travels 120 km by train and rest by car. He takes 20 minutes more if he travels 200 km by train and rest by car. Find the speed of the train and the car.

Philoid · Accepted Answer

Let the speed of the train be x km/h and that of the car be y km/h

Also, we know that time =

In situation 1, time spent travelling by train = h

And time spent travelling by car = h

So, total time taken in 8hour journey is

=

⇒ …I

Again, when he travels 200km by train and rest by car

Time taken by him travel 200km by train = h

And time spent travelling by car = h

Total time taken =

But given time of journey is 8hrs 20 min i.e = h

So, …II

Let = a and = b

30a + 120b = 2 …III

200a + 400b = …IV

Multiply Eq. III by 20 and Eq. IV by 3

600a + 2400b = 40

600a + 1200b = 25

_- - - _

1200b = 15

b =

substitute value of b in Eq. III

30a + 120 × = 2

a =

but, ⇒ x = 60

⇒ y = 80

Speed of train = 60 km/h

Speed of car = 80 km/h