SOLUTION: Hi, Thank you for answering my question in advance. A trucker calculates that if he increased his average speed by 20 km/hr, he could travel his 800 km route in 2.0 hours les

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi, Thank you for answering my question in advance. A trucker calculates that if he increased his average speed by 20 km/hr, he could travel his 800 km route in 2.0 hours les      Log On


   

Question 1010958: Hi,
Thank you for answering my question in advance.
A trucker calculates that if he increased his average speed by 20 km/hr, he could travel his 800 km route in 2.0 hours less time than usual. Find his usual speed.
Thank you
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28r=unknownUsualSpeed%2Ct=unknownUsualTime%2Ch=2%2Ck=20%2Cd=800%29 
          rate      time       distance
IF        r+k       t-h         d
USUAL     r          t          d

System of equations to solve for t and r:
system%28%28r%2Bk%29%28t-h%29=d%2Crt=d%29

STEPS FOR SOLVING - ARITHMETIC
rt%2Bkt-hr-kh=d
substitute for d using "usual" equation;
rt%2Bkt-hr-kh=rt
kt-hr-kh=0
t=%28hr%2Bkh%29%2Fk
Again use the "usual" equation, now substituting for t.
r%28hr%2Bkh%29%2Fk=d
r%28hr%2Bkh%29=kd
hr%5E2%2Bkhr=kd
highlight_green%28hr%5E2%2Bkhr-kd=0%29------almost to a formula for r. You can decide when you want to
make the substitutions for the given values. Continue symbolically from here and substitute later,
or do the substitutions now, and continue the arithmetic either way.
-

Substituting now, and get
after simplifying,
r%5E2%2B20r-8000=0

Formula for general solution of quadratic equation gives highlight%28r=80%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
Thank you for answering my question in advance.
A trucker calculates that if he increased his average speed by 20 km/hr, he could travel his 800 km route in 2.0 hours less time than usual. Find his usual speed.
Thank you
Let normal speed be S

Then increased speed = S + 20

We then get the following TIME equation: 800%2FS+=+800%2F%28S+%2B+20%29+-+2

800(S + 20) = 800S – 2S(S + 20) ------- Multiplying by LCD, S(S + 20)

800S+%2B+16000+=+800S+-+2S%5E2+-+40S

2S%5E2+-+800S+%2B+40S+%2B+800S+%2B+16000+=+0

2S%5E2+%2B+40S+%2B+16000+=+0

2%28S%5E2+%2B+20S+%2B+8000%29+=+2%280%29

S%5E2+%2B+20S+%2B+8000+=+0

(S - 80)(S + 100) = 0     

S, or normal speed = highlight_green%2880%29 km/h     OR      S = - 100 (ignore)