SOLUTION: train A travels 20mph slowr than Train B. It takes Train A 30min. longer than train B to travel 200 miles. how long does it take train A to make the 200mile trip? how long does

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Question 567233: train A travels 20mph slowr than Train B. It takes Train A 30min. longer than train B to travel 200 miles.
how long does it take train A to make the 200mile trip? how long does it take train B to travel 535 miles??
Found 2 solutions by mananth, lwsshak3:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
Train B speed = xmph
Train A speed = x-20 mph
Time taken by B = Time taken by A -1/2
t=d/r
200/x = 200/(x-20)-1/2
200/x -200/(x-20)=-1/2
LCD = x(x-20)
multiply equation by the LCD
200(x-20)-200*x=- 1/2 * x(x-20)
200x-4000-200x=-1/2*( x^2-20x)
multiply by -2
-400x+8000 +400x=x^2-20x
x^2-20x-8000=0
x^2-100x+80x-8000=0
x(x-100)+80(x-100)=0
(x-100)(x+80)=0
x=100 OR -80
Ignore negative since speed cannot be negative
spped of B is 100 mph
Time taken by B to travel 535 miles= 535/100
= 5.35 hours

Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
train A travels 20mph slowr than Train B. It takes Train A 30min. longer than train B to travel 200 miles.
how long does it take train A to make the 200mile trip? how long does it take train B to travel 535 miles??
**
let x=speed(mph) of train B
x-20=speed(mph) of train A
travel time = distance/speed
..
200/(x-20)-200/x=30min=1/2 hr
LCD:2x(x-20)
2x(200)-200*2(x-20)=x(x-20)
400x-400x+8000=x^2-20x
x^2-20x-8000=0
(x-100)(x+80)=0
x+80=0
x=-80(reject, x>0)
or
x-100=0
x=100 mph (speed of train B)
x-20=80 mph (speed of train A)
..
travel time of train A=200/80=2.5 hrs
travel time of train B=535/100=5.35 hrs
.
ans:
time it takes train A to make the 200mile trip=2.5 hrs
time it take train B to travel 535 miles=5.35 hrs