Quadratic Equation Solution24





In this page quadratic equation solution24 we are going to see solution of the word problems of the topic quadratic equation.

Question 31

An express train makes run 240 km t a certain speed. Another train whose speed is 12 km/hr less takes an hour longer to make the same trip. Find the speed of the express train.

Solution:

Let “x” be speed of express train

Another train whose speed is 12 km/hr less than the speed of express train

So “x – 12” be the speed of another train

Distance to be covered = 240 km

Let T1 be the time taken by the train to cover the distance 240 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 + 12) km/hr

Time = Distance /speed

T1 = 240/x

T2 = 240/(x - 12)

T2 - T 1 = 1 hour

[240/(x- 12)] - [240/x] = 1

240[(1/(x -12) - 1/x] = 1

240[(x - x + 12)/x(x - 12)] = 1

240[12/(x² - 12 x)] = 1

2880 = (x² - 12 x)

x² - 12 x - 2880 = 0

x² + 60 x - 48 x - 2880 = 0

x(x + 60)- 48 (x + 60) = 0

(x - 48) (x + 60) = 0

x - 48 = 0           x + 60 = 0

 x = 48              x = -60

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

Speed of express train = 48 km/hr

Speed other train = (x - 12) = (48 - 12) = 36 km/hr


Verification:

Time = Distance/speed

Time taken by the express train to cover 240 km = 240/48

                                                                     = 5 hours

Time taken by the another train to cover 240 km = 240/36

                                                              = 6 hours

difference of time taken = 6 - 5 = 1 hour

quadratic equation solution24