Word Problem Solution6





In this page word problem solution6 we are going to see solution for first word problem of the worksheet cross multiplication method.

Formulate the following problems as a pair of equations,and hence find their solutions:

(vi) A train traveled a certain distance at a uniform speed. If the train had been 6 km/hr faster,it would have taken 4 hours less than the scheduled time. If the train were slower by 6km/hr, then it would have taken 6 hours more than the scheduled time. Find the distance covered by the train.

Let x km/hr be the speed of train

Let y be the time taken by the train

Distance = speed x time

             = x y

To form the first equation let us consider the given information from the question that is If the train had been 6 km/hr faster,it would have taken 4 hours less than the scheduled time.

it clearly says that speed is increased by 6 and time is reduced by 4

So ,     (x + 6) (y - 4) = x y  

      x y - 4 x + 6 y - 24 = x y

     x y - x y - 4 x + 6 y = 24

           - 4 x + 6 y = 24

divided by (-2) => 2 x - 3 y = -12  ----- (1)

To form the second equation let us consider the given information from the question that is If the train were slower by 6km/hr, then it would have taken 6 hours more than the scheduled time.

it clearly says that speed is reduced by 6 and time is increased by 6

So ,     (x - 6) (y + 6) = x y  

      x y + 6 x - 6 y - 36 = x y

     x y - x y + 6 x - 6 y = 36

              6 x - 6 y = 36

divided by (6) => x - y = 6  ----- (2)

                         2 x - 3 y = -12

          (2) x 2 => 2 x - 2 y =  12

                         (-)   (+)     (-) 

                        ---------------

                               - y = -24

                                 y = 24

Now we have to apply the value of y in the first equation to get value of x

Substitute y = 24 in the first equation we get

2 x - 3 (24) = -12

2 x - 72 = -12

2 x = -12 + 72

2 x = 60

  x = 60/2

  x = 30

Speed of the train = 30 km/hr

Time taken by the train = 24 hours

Distance covered by the train = x y = 30 x 24 = 720 km

Verification:

2 x – 3 y = -12 

2(30) - 3(24) = -12

60 - 72 = -12

-12 = -12

word problem solution6 word problem solution6


Try other questions

(i) One number is greater than thrice the other number by 2. If 4times the smaller number exceeds the greater by 5, find the numbers. Solution

(ii) The ratio of income of two persons is 9:7 and the ratio of their expenditure is 4:3.If each of them manages to save $2000 per month, find their monthly income.  Solution

(iii) A two digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the given number. Find the given number.  Solution

(iv) Three chairs and two tables cost $700 and five chairs and three tables cost $1100.What is the total cost of 2 chairs and 3 tables.  Solution

(v) In a rectangle,if the length is increased and breadth is reduced each by 2 cm then the area is reduced by 28 cm ². If the length is reduced by 1 cm and the breadth is increased by 2 cm,then the area increases by 33cm². Find the area of the rectangle.   Solution