ii) A passenger train takes 2 hours more than an
express train to travel a distance of 240 km. The
speed of the express train is more than that of
passenger train by 20 km/h. Find the speed of
both the trains.
Answers
Answer:-
Let the Speed of the passenger train be "x" km/h and time taken by the express train to cover the distance be "t" hours.
Given:
Total Distance = 240 km
Speed of the passenger train = x km/h
Time taken by the passenger train to cover the distance = (t + 2) hrs.
Speed of the express train = (x + 20) km/h
Time taken by the express train to cover the distance = t hrs.
We know that,
Distance = Speed * time.
For speed of passenger train,
→ 240 = (x)*(t + 2)
→ 240 = tx + 2x
→ 240 - 2x = tx
→ (240 - 2x)/x = t -- equation (1)
For speed of Express train,
→ 240 = (t) (x + 20)
→ 240 = tx + 20t
Substitute the value of "t" here.
→ 240 = (240 - 2x)/x * x + 20( 240 - 2x)/x
→ 240 = (240 - 2x)/x + 4800 - 40x/x
→ 240 = (240x - 2x² + 4800 - 40x)/x
→ 240x - 240x = - 2x² - 40x + 4800
→ 0 = - 2x² - 40x + 4800
→ 2x² + 40x - 4800 = 0
→ 2x² - 80x + 120x - 4800 = 0
→ 2x(x - 40) + 120(x - 40) = 0
→ (2x + 120)(x - 40) = 0
2x + 120 = 0
→ 2x = - 120
→ x = - 120/2
→ x = - 60
x - 40 = 0
→ x = 40
Speed can't be negative hence positive value is taken i.e., 40 km/h
Therefore,
Speed of the passenger train = x = 40 km/h.
Speed of the express train = x + 20 = 60 km/h.