SOLUTION: A train travels 110 km in the same time that a plane covers 385 km. If the speed of the plane is 30 km per hr less than 4 times the speed of the train, find both speeds.

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Question 924155: A train travels 110 km in the same time that a plane covers 385 km. If the speed of the plane is 30 km per hr less than 4 times the speed of the train, find both speeds.
Found 2 solutions by TimothyLamb, MathTherapy:
Answer by TimothyLamb(4379)   (Show Source): You can put this solution on YOUR website!
x = speed of airplane
y = speed of train
---
s = d/t
t = d/s
---
airplane time:
t = 385/x
---
train time:
t = 110/y
---
t = 385/x = t = 110/y
385/x = 110/y
385y = 110x
---
x = 4y - 30
---
385y = 110x
x = 4y - 30
---
put the system of linear equations into standard form
---
110x - 385y = 0
x - 4y = -30
---
copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
solution:
x = speed of airplane = 210 kph
y = speed of train = 60 kph
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
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Solve systems of linear equations up to 6-equations 6-variables:
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Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

A train travels 110 km in the same time that a plane covers 385 km. If the speed of the plane is 30 km per hr less than 4 times the speed of the train, find both speeds.


Let speed of train be S

Then speed of plane is: 4S – 30

Time it takes train to travel 110 km: 

Time it takes plane to travel 385 km: 

Since they cover their respective distances in the same amount of time, we then get:



110(4S – 30) = 385(S) ------- Cross-multiplying

440S – 3,300 = 385S

440S – 385S = 3,300

55S = 3,300

S, or speed of train = , or  km/h 

Speed of plane = 4(60) – 30, or 240 – 30, or  km/h

You can do the check!! 

===================

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