Word problem on rate/time/distance

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kimmy

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Nov 12, 2005
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Can someone help me please? This is the word problem I have:

Jeff rode his bike 45 miles to get to the part, and his co-worker Chris rode his bike 70 miles to meet Jeff at the park. Chris averaged 5mph more than Jeff and his trip took one-half hour longer than Jeff. How fast was each traveling?

I know that D=RT and R=T/D.

Jeff = T/45 and therefore Chris's rate is Jeff+5 = T/70

I am stuck from here. Without simply guessing at numbers and plugging values to eventually find an answer.

Can someone help by showing me the steps to figure this out. I am not looking for the final answer, just the equation set up or way to solve for their rate of travel. I would like to figure it out myself.

Thanks!
 
you have 2 equations, one for each person, that ivolve 3 variables. D,T & R.

start with this information:

jeff-
D=45
R=x
T=y

chris-
D=70
R=x+5
T=y+1/2

See if you can use this information with you 2 equations to cancel out variables and solve.
 
You're on the right track (and thank you for showing your reasoning!!), but I think you omitted the "time" information. Try this:

. . . . .jeff:
. . . . .distance: 45
. . . . .rate: r
. . . . .time: t = 45/r

. . . . .chris:
. . . . .distance: 70
. . . . .rate: r + 5
. . . . .time: t + 0.5 = 70/(r + 5)

Then Chris' "time" expression may be solved for "t=" to get:

. . . . .t = 70/(r + 5) - 0.5

We now have two expressions for "t":

. . . . .45/r = 70/(r + 5) - 0.5

Solve for "r".

Alternate method using same initial set-up:

. . . . .(chris' time) is (jeff's time) plus (another half hour)

...which translates as:

. . . . .70/(r + 5) = 45/r + 0.5

This is the same as the previous equation; the "0.5" was added over to Jeff's side.

Hope that helps.

Eliz.
 
Thank You

Thank You Thank You....it helps very much. I had got halfway there on my own, it was the -.05 on Chris's time where I got stuck.

Kim
 
Here is what I got

70/r+5-45/r=1/2

LCD = 2r(r+5), so multiply all by LCD
[2r(r+5)(70/r+5)]-[2r(r+5)(45/r)]-1/2[2r(r+5)]

= 140r-90r-450=r^2+5r
=-r^2-45r-450=0
=r^2+45r+450

am I on the right track?
 
Re: Here is what I got

kimmy said:
70/r+5-45/r=1/2

LCD = 2r(r+5), so multiply all by LCD
[2r(r+5)(70/r+5)]-[2r(r+5)(45/r)]-1/2[2r(r+5)]

= 140r-90r-450=r^2+5r
=-r^2-45r-450=0
=r^2+45r+450
am I on the right track?
Click to expand...
First, your 70/r+5-45/r=1/2 needs brackets: 70/(r+5) - 45/r = 1/2

You ended up close; should be r^2 - 45r + 450 = 0
Solve that and you'll get 2 valid solutions.

Could be done this way (I find easier):
70/(r+5) - 45/r = 1/2
70/(r+5) = 45/r + 1/2
70/(r+5) = (r+90)/2r
Now crisscross multiply to get (r+5)(r+90) = 140r : r^2 - 45r + 450 = 0

Hint: before going to the quadratic, see if you can factor:
15 and 30 look like good candidates, right?
 
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