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

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“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:

It subtracts sadness and adds happiness in our life.

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”