A freight train covered 120 miles at a certain speed Had the

A freight train covered 120 miles at a certain speed. Had the train been able to travel 10 mph faster, the trip would have been 2 hours shorter. How fast did the train go?

Solution

D=RT
D/R=T
120/X=T
120/(X+10)=T-2
NOW REPLACE T WITH 120/X IN THE SECOND EQUATION & SOLVE FOR X.
120/(X+10)=(120/X)-2
120/(X+10)=(120-2X)/X NOW CROSS MULTIPLY.
(X+10)(120-2X)=120X
120X+1200-20X-2X^2=120X
-2X^2+100X+1200-120X=0
-2X^2-20X+1200=0
-2(X^2+10X-600)=0
-2(X-20)(X+30)=0
X-20=0
X=20 MPH. ANS. FOR THE FIRST 120 MILE TRIP.
20+10=30 MPH. ANS. FOR THE FASTER TRIP.
PROOF:
120/30=(120/20)-2
4=6-2
4=4