I really need major help with word problems... Please if anyone can guide me with how these things are worked out, would really appreciate:

The first problem : Fred drove home to the airport 320 km away at an average speed. If he had increased his average speed by 1km/h, he would have taken 20 mins less. What was his average speed?

This is under the topic of quadratic equation word problems. Please help. Thanks

Question

I really need major help with word problems... Please if anyone can guide me with how these things are worked out, would really appreciate:

The first problem :  Fred drove home to the airport 320 km away at an average speed.  If he had increased his average speed by 1km/h, he would have taken 20 mins less.  What was his average speed?

This is under the topic of quadratic equation word problems.  Please help. Thanks

ajprincess · Answer

Let us say the average speed is s.
The distance between the home and the airport is 320km. Also let us say that time taken to cover that distance with the speed s is t.
speed=distance/time
s=320/t
t=320/s
the increased speed=s+1
new time=t-20
distance is the same.
s+1=320/(t-20)
(s+1)*(t-20)=320
t-20=320/(s+1)
t=320/(s+1)+20
320/(s+1)+20=320/s
does this help?

ajprincess · Answer

@miszery

anonymous · Answer

okay thanks let me study it a bit lol i'm slow

ajprincess · Answer

oh k. take your own time:)

anonymous · Answer

ooh okay i see cool :)

anonymous · Answer

do you want to help me with more word problems @ajprincess  :PP

ajprincess · Answer

well sure:) have u solved this one?

anonymous · Answer

30.5 km /h ?

anonymous · Answer

trying to figure out how to use the quadratic equation to solve that atm

ajprincess · Answer

pls wait a sec

ajprincess · Answer

ooops reallly sorrry. I made a mistake. let me correct it

anonymous · Answer

yeah teh teacher has only the answer but not showing the working :(

anonymous · Answer

okay

ajprincess · Answer

Let us say the average speed is s.
The distance between the home and the airport is 320km. Also let us say that time taken to cover that distance with the speed s is t.
speed=distance/time
s=320/t
t=320/s
the increased speed=s+1
upto this 5n.

anonymous · Answer

here is the answer she gave:   320/x   -    320/x+1     =    1/3          how did she get  1/3  ?

ajprincess · Answer

20 minutes will be 1/3 of a hour.
60minutes in an hour.
20/60=1/3

anonymous · Answer

ooh

anonymous · Answer

righto thats clearer L:D

anonymous · Answer

can u show me how to turn this into a quadratic equation?

anonymous · Answer

$$320x + 320 - 320x \div x ^{2}+x   =   1/3 (x ^{2}+x)   \right?$$

anonymous · Answer

ew yuk

anonymous · Answer

|dw:1366034757086:dw|

anonymous · Answer

oh ok

ajprincess · Answer

is that clear?

anonymous · Answer

yep thanks :)))

ajprincess · Answer

using quadratic formula u can solve it. do u knw it?

anonymous · Answer

yes i know this part hehehe.. just putting the numbers into that equation is hard for me

anonymous · Answer

but once its in that form I can solve it

ajprincess · Answer

so the new time will be
t-1/3.
distance is the same.
s+1=320/(t-20)
(s+1)*(t-20)=320
t-1/3=320/(s+1)
t=320/(s+1)+1/3
320/(s+1)+1/3=320/s
1/3=320/s-320/(s+1)
      =320(1/s-1/(s+1))
       =320((s+1-s)/s(s+1))
      =320(1/(s(s+1)))
1*(s(s+1))=320*3
s^2+s=960
s^2+s-960=0

ajprincess · Answer

reallly sorrry for messing it up. nw is the above one clear? it is the correct one. if it is nt cleat pls ask.

ajprincess · Answer

Did ur teacher give u the final answer for the average speed?

ajprincess · Answer

@miszery

anonymous · Answer

yes sorry   30.5 km

anonymous · Answer

@ajprincess

ajprincess · Answer

hmm. i guess that's the answer u will get u solve the quadratic equation s^2+s-960=0