SOLUTION: a car traveled 1520 miles at a certain speed. if the speed had been 19 mph faster, the trip could have been made in 4 hr less time. find the speed

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: a car traveled 1520 miles at a certain speed. if the speed had been 19 mph faster, the trip could have been made in 4 hr less time. find the speed       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 528583: a car traveled 1520 miles at a certain speed. if the speed had been 19 mph faster, the trip could have been made in 4 hr less time. find the speed
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a car traveled 1520 miles at a certain speed.
If the speed had been 19 mph faster, the trip could have been made in 4 hr less time.
find the speed
:
Let s = the speed
then
(s+19) = the faster speed
:
Write a time equation: time = dist/speed
:
Actual speed time - faster speed time = 4hrs
1520%2Fs - 1520%2F%28%28s%2B19%29%29 = 4
Multiply by s(s+19) to get rid of the denominators, results:
1520(s+19) - 1520s = 4s(s+19)
:
1520s + 28880 - 1520s = 4s^2 + 76s
a quadratic equation
4s^2 + 76s - 28880 = 0
simplify, divide by 4
s^2 + 19s - 7220 = 0
You can use the quadratic formula here, but this will factor to
(s+95)(s-76) = 0
the positive solution
s = 76 mph was his speed
:
:
See if that is true, find the actual times
1520/76 = 20 hrs
1520/95 = 16 hrs
----------------
differs = 4 hrs