Question 461946
Two trains are traveling at 250 miles apart and traveling towards each other . They meet in 4 hours . If one train's speed is 10 miles faster than the other . Find the speed of both trains.
..
let x=speed of one train
x+10 = speed of other faster train
travel time = distance/speed
travel time of slower train=250/x
travel time of faster train=250/(x+10)
250/x+250/(x+10)=4
LCD:x(x+10)
250x+2500+250x=4x^2+40x
4^x^2-460x-2500=0
divide by 4
x^2-115-625=0
solve by quadratic formula:
a=1, b=-115, c=-625
x=[-(-115)ħsqrt((-115)^2-(4*1*-625)]/2*1
x=[115ħsqrt(15725)]/2
x=[115ħ125.4]/2
x=120.2
or
x=-5.2 (reject, x>0)
ans:
speed of slower train=120.2 mph
speed of faster train=130.2 mph