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.

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the distance formula: d+=+r%2At where d = distance, r = rate/speed, and t = time of travel.
For the train:
d%5B1%5D+=+r%5B1%5D%2At Substitute d = 120km
120+=+r%5B1%5D%2At Rewrite this as:highlight_green%28t+=+120%2Fr%5B1%5D%29 and substitute into the equation for d%5B2%5D.
For the plane:
d%5B2%5D+=+r%5B2%5D%2At Notice that t (time) is the same in both cases. Substitute d = 336km and r%5B2%5D+=+3r%5B1%5D-10
336+=+%283r%5B1%5D-10%29%2At Substitute, from above, highlight_green%28t+=+120%2Fr%5B1%5D%29
336+=+%28%283r%5B1%5D%29-10%29%28highlight_green%28120%2Fr%5B1%5D%29%29 Multiply both sides byr%5B1%5D
336%2Ar%5B1%5D+=+%28%283r%5B1%5D%29-10%29%2A120%29 perform the indicated multiplication on the right side.
%28336%29%2Ar%5B1%5D%29+=+360r%5B1%5D-1200 Add 1200 to both sides.
1200%2B336r%5B1%5D+=+360r%5B1%5D Subtract 336r%5B1%5D from both sides.
1200+=+24r%5B1%5D Divide both sides by 24.
50+=+r%5B1%5D and r%5B2%5D+=+3%2850%29-10
r%5B1%5D+=+50km/hr. and
r%5B2%5D+=+140km/hr.
The train is going 50km/hr. and the plane is going 140km/hr.

Answer by drj(1380) About Me  (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. distance+=+speed+%2A+time and speed+=+distance%2Ftime

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

Step 3. Let 336%2Ft be the speed of the plane traveled in 336 km with the same time t.

Step 4. Then 336%2Ft=3%2A120%2Ft-10 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.

t%2A336%2Ft=t%2A3%2A120%2Ft-t%2A10

336=360-10t

Add 10t-336

336%2B10t-336=360-10t%2B10t-336

10t=24

Divide 10 to both sides of the equation

10t%2F10=24%2F10

t=2.4 Then 120%2F2.4=50 and 336%2F2.4=140

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.

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Good luck in your studies!

Respectfully,
Dr J