In this page quadratic equation practical solution5 we are going to see solution of practice question of the worksheet quadratic equation practical application.

Question 5:

A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hr more, it would have taken 30 minutes less for the journey. Find the original speed of the train.

Solution:

Let “x” be the usual speed of the train

Let T1 be the time taken to cover the distance 90 km in the speed x km/hr

Let T2 be the time taken to cover the distance 90 km in the speed (x + 15) km/hr

Time = Distance/Speed

T1 = 90/x

T2 = 90/(x + 15)

By using the given condition

T1 - T2 = 30/60

(90/x)- (90/(x + 15)) = ½

Taking 90 commonly from two fractions

90 [ (1/x) – 1/(x+15) ] = ½

(X + 15 – x)/x(x + 15)  = 1/(90 x 2)

15/x² + 15 x  = 1/180

15 (180) = 1(x² + 15 x)

x² + 15 x = 2700

x² + 15 x – 2700 =  0

x² + 60 x - 45 x  – 2700 =  0

x (x + 60) - 45 (x + 60) = 0

(x - 45) (x + 60) = 0

x – 45 = 0               x + 60 = 0

x = 45                      x = -60

Therefore speed of the train is 45 km/hr

Question 6     Question 7     Question 8     Question 9     Question 10

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: