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.
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.

Philoid · Accepted Answer

Let the speed of the boat in still water be x km/h and speed of the stream be y km/h

Speed of boat upstream = (x – y) km/h

Speed of boat downstream = (x + y) km/h

But, total time of journey is 10hrs.

= 10

= 13

Let be a and be b

30a + 44b = 10 …I

40a + 55b = 13 …II

Multiply Eq. I by 4 and Eq. II by 3

120a + 176b = 40

120a + 165b = 39

_- - - _

11b = 1

b =

substituting value of b in Eq. I

30a + 44× = 10

⇒ 30a + 4 = 10

⇒ 30a = 6

⇒ a =

∴ ⇒ ⇒ 5 = x + y ⇒ 5 = x + y

∴ ⇒ ⇒ 11 = x - y ⇒ 11 = x - y ….IV

x + y = 5

x – y = 11

2x = 16

x = 8

substitute value of x in Eq. III

8 + y = 5

Y = 3

Hence, Speed of boat = 8 km/h;

Speed of stream = 3 km/h