SOLUTION: . to travel from singapore to kuala lampur ,a distance kf 390km , motoridt finds that if he travels 6 km/h faster than its usual average speed,he will take 15 minutes less ti compl

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: . to travel from singapore to kuala lampur ,a distance kf 390km , motoridt finds that if he travels 6 km/h faster than its usual average speed,he will take 15 minutes less ti compl      Log On


   

Question 1011058: . to travel from singapore to kuala lampur ,a distance kf 390km , motoridt finds that if he travels 6 km/h faster than its usual average speed,he will take 15 minutes less ti complete his usual journey . Calculate the usual avergae speed of the motorist
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This form of travel rates problem is common as an exercise. 
           rate     time      distance
IF         r+6      t-1/4      390
Usual      r        t          390


           rate     time      distance
IF         r+k      t-h        d
Usual      r        t          d

Be sure you understand what is happening in and between the two data tables above.

system%28%28r%2Bk%29%28t-h%29=d%2Crt=d%29

rt%2Bkt-hr-hk=d
d%2Bkt-hr-hk=d
kt-hr-hk=0
kt=hr-hk
t=%28hr-hk%29%2Fk------formula for t in terms of r

rt=d
r=d%2Ft
r=d%2A%281%2Ft%29
r=d%28k%2F%28hr-hk%29%29
r%28hr-hk%29=dk
highlight_green%28hr%5E2-hkr-dk=0%29-----quadratic equation in the unknown variable, r.
You can use the formula for general solution of a quadratic equation and try to simplify
that, if at all possible, ... or you can simply substitute the given, known values for h
, k, and d, now and then deal with the resulting form of quadratic equation.

%281%2F4%29r%5E2-%281%2F4%29%2A6r-390%2A6=0
%281%2F4%29r%5E2-%283%2F2%29r-2340=0
highlight_green%28r%5E2-6r-9360=0%29----now the quadratic equation is less general, fewer symbols.

r=%286%2B-+sqrt%2836%2B4%2A9360%29%29%2F2

r=%286%2B-+sqrt%2837476%29%29%2F2
r=%286%2B-+sqrt%284%2A9%2A3%2A347%29%29%2F2
r=%286%2B-+2%2A3sqrt%283%2A347%29%29%2F2----you need the PLUS form.
highlight%28r=3%2B3sqrt%283%2A347%29%29
Do whatever you need with this value.

--
347 and 3 both are prime numbers. Decimal approximate for the solution is highlight%28r=99.8%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
. to travel from singapore to kuala lampur ,a distance kf 390km , motoridt finds that if he travels 6 km/h faster than its usual average speed,he will take 15 minutes less ti complete his usual journey . Calculate the usual avergae speed of the motorist
Let usual speed be S

Then hypothetical speed = S + 6

We then get the following TIME equation: 390%2FS+=+390%2F%28S+%2B+6%29+%2B+15%2F60_______390%2FS+=+390%2F%28S+%2B+6%29+%2B+1%2F4

390(4)(S + 6) = 390S(4) + S(S + 6) -------- Multiplying by LCD, 4S(S + 6)

1560S+%2B+9360+=+1560S+%2B+S%5E2+%2B+6S	

S%5E2+%2B+6S+%2B+1560S+-+1560S+-+9360+=+0

S%5E2+%2B+6S+-+9360+=+0	

Continue to solve for S, the usual speed, ignoring the negative (< 0) value for S