SOLUTION: A train travels 120 km in the same time that a plane covers 336 km. If the speed of the the plane is 10 km per hour less than 3 times the speed of the train, find both speeds.

Question 224529: A train travels 120 km in the same time that a plane covers 336 km. If the speed of the the plane is 10 km per hour less than 3 times the speed of the train, find both speeds.
Found 2 solutions by Earlsdon, drj:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Start with the distance formula: where d = distance, r = rate/speed, and t = time of travel.
For the train:
Substitute d = 120km
Rewrite this as: and substitute into the equation for .
For the plane:
Notice that t (time) is the same in both cases. Substitute d = 336km and
Substitute, from above,
Multiply both sides by
perform the indicated multiplication on the right side.
Add 1200 to both sides.
Subtract from both sides.
Divide both sides by 24.
and
km/hr. and
km/hr.
The train is going 50km/hr. and the plane is going 140km/hr.
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
A train travels 120 km in the same time that a plane covers 336 km. If the speed of the the plane is 10 km per hour less than 3 times the speed of the train, find both speeds.

Step 1. and

Step 2. Let be the speed of the train where t is the time traveled in 120 km.

Step 3. Let be the speed of the plane traveled in 336 km with the same time t.

Step 4. Then since the speed of the the plane is 10 km per hour less than 3 times the speed of the train,

Step 5. Multiply by t to both sides of the equation.

Add 10t-336

Divide 10 to both sides of the equation

Then and

Also, note that the plane's speed is 10km/hour less than 3 times the speed of the train.

Step 6. ANSWER: The speed of the train is 50 km/hr and the plane's speed is 140 km/hr.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

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