A train covered a certain distance at a uniform speed. If the train would have been 10km/hr faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10km/hr; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
Answers
Answer:
Let the speed of the train be xkm/h and the time taken by train to travel the given distance be t hours and the distance to travel be dkm. We know that,
⇒Speed=
Time /Distance
⇒x=
t /d
∴d=xt.......(i)
Case 1
⇒(x+10)×(t−2)=d
⇒xt+10t−2x−20=d
⇒d+10t−2x−20=d
⇒−2x+10t=20...... (ii)
Case 2
⇒(x−10)×(t+3)=d
⇒xt−10t+3x−30=d
⇒d−10t+3x−30=d
⇒3x−10t=30......... (iii)
Adding equations (ii) and (iii), we gets
⇒x=50
Substitute the value of x in (ii) we gets
⇒(−2)×(50)+10t=20
⇒−100+10t=20
⇒10t=120
⇒t=12 hours
Substitue the value of t and x in equation (i), we gets
Distance to travel =d=xt
⇒d=12×50=600Km
Hence, the distance covered by the train is 600km.
Step-by-step explanation:
- Speed = x = 50
- Time = y = 12
- Distance = 600 km
Step-by-step explanation:
- Distance = Speed × Time
Let,
- Speed be 'x' and Time be 'y'
- Distance = xy -------- (1)
We know that,
- Distance = (x - 10) (y + 3) -------- (2)
- Distance = (x - 10) (y - 3) -------- (3)
⟼ xy = xy - 10y + 3x - 30
⟼ 3x - 10y = 30 --------- (4)
Solving (3),
⟼ xy = xy + 10y - 2x - 20
⟼ -2x + 10y = 20 -------- (5)
Adding (4) & (5),
3x - 10y = 30
-2x + 10y = 20
___________
x = 50
___________
Substituting 'x' in (4),
⟼ 3x - 10y = 30
⟼ 3 (50) - 10y = 30
⟼ 150 - 10y = 30
⟼ 10y = 150 - 30
⟼ 10y = 120
⟼ y = 120 / 10
⟼ y = 12
Substituting 'x' & 'y' in (1),
⟼ Distance = xy
⟼ Distance = 50 × 12
⟼ Distance = 600 km
- ∴ Distance = 600 km