Question

A train travels a distance of 180kms at acertain averagespeed. had this speed been 4 km/hr less,the time would have increased by 1/2 hr. determine the train`s average speed.

Answer 1

Answer:

Original Speed of train = 40 km/h

Step-by-step explanation:

Let the original speed of train be x

distance  = 180 kms

Time taken with original speed = 180/x   [ time = Distance/speed]

Now, Speed is decreased by 4km/h

New Speed of train = x - 4

Distance is same = 180 km

Time taken with new speed = 180/(x-4)

According to question With New Speed it takes 1/2 hour more

∴ Time with new speed - time with old speed = 1/2

$\frac{180}{(x - 4)} - \frac{180}{x} = \frac{1}{2}$

$\frac{180x - 180(x-4)}{x(x-4)}=\frac{1}{2}$

$\frac{180x - 180x+720)}{x^2-4x}=\frac{1}{2}$

2× 720 = x² - 4x

x² - 4x - 1440 = 0

Splitting Middle Term

x² - 40x + 36x - 1440 = 0

Taking x common from first two terms and 36 from last two terms

x (x - 40) + 36 ( x - 40) = 0

(x - 40 ) ( x + 36) = 0

x - 40 = 0            x + 36 = 0

x = 40                 x = - 36 (Speed can not be negative so ignoring this value)

∴ Original Speed of train = 40 km/h