Notice that the time for both trips is the SAME but not known (let's use the letter T to address this unknown).
We also assign St to the speed of the train, and Sp to the speed of the plane.
Then, the relationship between the speeds according to the information they provide, is given by the equation:
Sp = 5 * St - 30
we also know that the train covers 140 km in the time T, Then according to the formula for speed (distance divided by time) we can say:
St = 140 km / T, therefore T = 140 km / St
We do something similar with the information on the distance covered by the plane:
Sp = 630 km / T which solving for T gives:
T = 630 km / Sp
Now we equal the expressions for T (since that time is the SAME as we noticed before, and get:
630 km / Sp = 140 / St
we corss-multiply to get the speeds in the numerator:
630 St = 140 Sp
ANd we use the very first equation we wrote (Sp = 5 * St - 30)
to replace Sp in terms of St:
630 St = 140 (5 St - 30)
Now use distributive property on the right to eliminate the parenthesis:
630 St = 700 St - 4200
add 4200 to both sides, and subtract 630 St from both sides :
4200 = 700 St - 630 St
4200 = 70 St
divide both sides by 70 to isolate St completely:
St = 4200 / 70
St = 60 km/h (this is the speed of the train)
Now we can find the value of the speed of the plane, using the first equation again:
Sp = 5 * St - 30 = 5 (60) - 30 = 300 - 30 = 270 km/h
Then the speed of the plane is: 270 km/h