A plane travel 100 kph faster than a train the plane covers

A plane travel 100 kph faster than a train the plane covers 500 km in the same time that train coves 300 km find the speed of each one?

Solution

The plane\'s characteristics are:
d = 500 km
r = x
t = same time as the train
.
The train\'s characteristics are:
d = 300 km
r = x - 100
t = same time as plane
.
Since the one thing that is equal is time, we can format each equation to isolate t.
.
For the plane:
t = d/r
t = 500/x
.
For the train:
t = d/r
t = 300/(x-100)
.
Now we can rely on the principle that if a=b and b=c, then a=c. Or \"equals are equal.\"
.
500/x = 300/(x-100)
.
Now we can cross-multiply
500 * (x-100) = 300 * x
.
Multiplying through on the left we have
500x - 50,000 = 300x
.
Subtracting 300x from both sides
200x -50,000 = 0
.
Adding 50,000 to both sides
200x = 50,000
.
Dividing both sides by 200
x = 250
.
Looking back at the setup, the train\'s speed is 250 - 100 = 150.