In this page quadratic equation solution22 we are going to see solution of the word problems of the topic quadratic equation.
Question 29
A train covers a distance of 300 km at a certain average speed. If its speed was decreased by 10km/hr, the journey would take 1 hour longer. What is the average speed.
Solution:
Let “x” be the average speed of the train
If its speed was decreased by 10km/hr, the journey would take 1 hour longer
So “x – 10” be the decreased speed
Time = Distance/Speed
Let T1 be the time taken by the train to cover the distance in the speed of x km/hr
Let T2 be the time taken by the train to cover the distance in the speed of (x - 10) km/hr
T1 = 300/x
T2 = 300/(x – 10)
T1 – T2 = 1
[300/x] - [300/(x-10)] = 1
300 [(1/(x - 10) – 1/(x)] = 1
300 [ x – x + 10]/[x (x -10)] = 1
3000/(x² – 10 x) = 1
3000 = x² – 10 x
x² – 10 x = 3000
x² – 10 x – 3000 = 0
x² – 60 x + 50 x – 3000 = 0
x (x – 60) + 50 (x – 60) = 0
(x + 50)(x – 60) = 0
x + 50 = 0 x – 60 = 0
x = - 50 x = 60
Here x represents the speed of the train. So we should not take the negative value - 50 for x.
So speed of the 60 km/hr
Verification:
Time taken by the train with speed 60 km/hr
Time = Distance/speed
= 300/60
= 5 hours
Time taken by the train with speed 50 km/hr
Time = Distance/speed
= 300/50
= 6 hours
difference between time taken = 6 - 5
= 1 hour
quadratic equation solution22