SOLUTION: A train travels 600 kilometers in the same time that a truck travels 520 kilometers. Find the speed of the train if the train's average speed is 8 kilometers per hour faster than t

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Question 246664: A train travels 600 kilometers in the same time that a truck travels 520 kilometers. Find the speed of the train if the train's average speed is 8 kilometers per hour faster than the truck's.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let x= rate of the truck
x+8= rate of the train
520 = distance of truck
600= distance of train

Time of Truck = Time of Train
D%2Fr=D%2Fr
520%2Fx=600%2F%28x%2B8%29

Since a%2Fb=c%2Fd means that ad=bc,
520%2Fx=600%2F%28x%2B8%29 means that 520%2A%28x%2B8%29=600%2Ax%29
520x+520*8=600x

Subtract 520x from each side:
520*8=80x
52=x

So, x= 52 km/hr = speed of truck
x+8= 60 km/hr = speed of train

Check:
520%2F52=600%2F60
It checks!

a) If x=6, then A=x^2 + 6x +8
A=6^2 +6*6+8
A=36+36+8
A= 80 square units

b) If A=x^2 +6x+8
A=(x+2)(x+4)

A= W*L
If x+2 = width, then L=x+4.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus