In this page quadratic equation solution25 we are going to see solution of the word problems of the topic quadratic equation.

**Question 32**

A train covers a distance of 600 km at x km/hr. Had the speed been (x + 20) km/hr, the time taken to cover the distance would have been reduced by 5 hours.Write the equation in x and solve it to calculate x.

**Solution:**

here “x” represents speed of train

if it had the speed (x + 20) km/hr the time taken to cover the distance would have been reduced by 5 hours

Distance to be covered = 600 km

Let T1 be the time taken by the train to cover the distance 600 km at the speed of x km/hr

Let T2 be the time taken by the train to cover the distance 240 km at the speed of (x + 20) km/hr

Time = Distance /speed

T1 = 600/x

T2 = 600/(x + 20)

T1 - T2 = 5 hours

[600/x] - [600/(x + 20)] = 5

600[(1/x - 1/(x + 20)] = 5

600[(x + 20 - x)/x(x + 20)] = 5

600[20/(x² + 20 x)] = 5

12000/5 = (x² + 20 x)

x² + 20 x - 2400 = 0

x² + 60 x - 40 x - 2400 = 0

x(x + 60) - 40 (x + 60) = 0

(x - 40) (x + 60) = 0

x - 40 = 0 x + 60 = 0

x = 40 x = -60

Here x represents the speed of the train. So we should not take the negative value - 60 for x.

Speed of train = 40 km/hr

Increased speed = (x + 20) = (40 + 20) = 60 km/hr

**Verification:**

Time = Distance/speed

Time taken by the express train to cover 600 km = 600/40

= 15 hours

Time taken by the train to cover 600 km in the increased speed = 600/60

= 10 hours

difference of time taken = 15 - 10 = 5 hours

quadratic equation solution25

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