two trains are 480 miles apart. They start at the same time, and travel towards one another. The difference between the speeds of the two train is 20 miles per hour. If the two trains meet after four hours, find the speed of the faster train. please can someone explain this
Answers
Q. two trains are 480 miles apart. They start at the same time, and travel towards one another. The difference between the speeds of the two train is 20 miles per hour. If the two trains meet after four hours, find the speed of the faster train.
Step-by-step explanation:
Let the slower train's speed be=x
Then faster train=x+20
Now, we know-
Dist=spd*time
Distance covered for the slower train
4*x=4x
Distance covered for the faster train
4(x+20)=4x+80
According to question
4x+4x+80=480
8x=480-80
8x=400
x=50
If slower train's speed=50 kmph,
Then faster train's speed=50+20=70 kmph.
CHECKING
Distance for first train=4x=4*50=200
Distance for second train=4x+80=200+80=280
Total Distance=200+280=480
Given : The distance between two trains , d = 480 miles. they start at the same time and travel towards each other.
the difference between the speeds , ∆v = 20 miles/hr
time taken to meet the trains, t = 4 hrs.
To find : the speed of faster train.
solution : let v₁ is the speed of faster train and v₂ is the speed of slower train.
because, ∆v = 20
⇒v₁ - v₂ = 20 ..,.........(1)
the trains travel towards each other.
so, distance travelled by first train + distance travelled by 2nd train = 480 miles
⇒v₁t + v₂t = 480 miles
⇒(v₁ + v₂) × 4hrs = 480 miles
⇒v₁ + v₂ = 480/4 = 120 ...........(2)
from equations (1) and (2) we get,
v₁ = 70 , v₂ = 50
Therefore speed of faster train is 70 miles/hr