Question 157616

Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r

Let r=speed of the London-to-Madrid plane (1st plane)
Then r+40=speed of the Madrid-to-London plane (2nd plane)

Distance 1st plane travels=r*1+r*0.5=r*1.5
Distance 2nd plane travels=(r+40)*0.5


Now we know that when the above two distances add up to 1260 mi, the two planes will be in the process of passing each other.  So, our equation to solve is:

1.5r+0.5(r+40)=1260  get rid of parens
1.5r+0.5r+20=1260  subtract 20 from each side
1.5r+0.5r+20-20=1260-20  collect like terms
2r=1240  divide each side by 2
r=620 mi/hr-------------------------speed of 1st plane
r+40=620+40=660 mi/hr-------------------speed of 2nd plane

CK
in 1.5 hr, 1st plane travels (1.5)(620)=930 mi
in 0.5 hr, 2nd plane travels (0.5)(660)=330 mi
930+330=1260
1260=1260

Hope this helps-----ptaylor