Q. 2 A3.9( 20 Votes )

# 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.

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

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PREVIOUSSolve each of the following pairs of equations by reducing them to a pair of linear equation.NEXTFormulate 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.

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