SOLUTION: A delivery truck follows a regular route that is 270 km. One day the driver begins the route half hour late. In order to finish on time, she drives the truck 6km/hr faster than usu

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Question 1171220: A delivery truck follows a regular route that is 270 km. One day the driver begins the route half hour late. In order to finish on time, she drives the truck 6km/hr faster than usual. What is the truck's usual speed
Found 4 solutions by Boreal, ikleyn, josgarithmetic, MathTherapy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
d=v*t
270=vt
and
270=(v+6)*(t-0.5)
therefore, vt=vt-0.5v+6t-3
and 0.5v=6t-3 so v=12t-6
therefore, 12t^2-6t-270=0 substituting
2t^2-t-45=0
(2t+9)(t-5)=0
t=5 hours
so normally the speed is 54 km/h
at 60 km/h, 6 km/h faster, the trip will take 4 1/2 hours.
54 km/h
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

The time equation is


     -  = .


Each term in the left side is the traveled time.


  in the right side represents half an hour time difference.


Reduce to quadratic equation and solve it using quadratic formula or factoring.



ANSWER.  54 km/h  and  60 km/h.


You are instructed and directed.

If you have questions, post them to me.

----------------

To see many other similar problems solved,  look into the lesson
    - Had a car move faster it would arrive sooner
in this site.




Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
             SPEED         TIME         DISTANCE

NORMAL          r          270/r         270

LATE          r+6          270/(r+6)      270

DIFFERENCE                  1/2

-------solve for r.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
A delivery truck follows a regular route that is 270 km. One day the driver begins the route half hour late. In order to finish on time, she drives the truck 6km/hr faster than usual. What is the truck's usual speed
Let truck's normal speed be S

Then usual time = 

We then get the following TIME equation: 

270(2)(S + 6) = 270(2S) + S(S + 6) ------ Multiplying by LCD, 2S(S + 6)



(S - 54)(S + 60) = 0

Normal speed of truck, or          OR          S = - 60 (ignore) 

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