help me convert this please

Question

samantha ran on a fitness track for 20 minutes and then walked for 10 mnutes Her running rate was 250 ft per minute faster than her walking rate If she rand and walked a total of 15,500 ft how fast did she run?

Answer 1

set up variables

 

Rr  = rate-running 

Wr = rate-walking

Tr  = time running = 20 min

Tw = time walking = 10 min

 

D  = total dist

 

D = 15,500 ft  = (Rr x Tr)  +  (Wr x Tw)         (dist = rate-running*time-running + rate-walking x time-walking)

 

but we know rate walking + 250 ft/min = rate running

using our variables

 

Wr + 250 = Rr     or    Wr = Rr - 250 

 

now, just plugging in the times, and (Rr - 250) for Wr, we have one equation with one unknown (Rr)

 

D = 15,500 = (Rr x 20) + (Rr - 250) x 10

 

                   = 20Rr + 10Rr - 2,500

 

add 2500 each side

 

      18,000 = 30Rr      or  Rr = 18,000/30 = 600 ft/min = running rate

 

as a check:

 

      15,500 ft = (Rr x Tr) + (Wr x Tw)  =  (600*20) + (600-250)*10       are these equal  ???

 

      15,500 ft =                                        12,000 + 3,500 = 15,500    yes

 

 

 

Answer 2

Hi Rina,

 

Let X = Samantha's walking rate in feet/minute

 

Then her running rate is X + 250 feet/minute

 

Distance = rate x time

 

So her running distance was (X + 250) (20)

 

Her walking distance was 10X

 

Her total distance was 15,500 feet

 

So let's add her running distance and walking distance:

 

(X+250)(20) + 10X = 15,500

 

20X + 5000 + 10X = 15500

 

30X + 5000 = 15500

 

30X = 10500

 

X = 350 feet/min

 

She ran 350 + 250 = 600 feet per minute

 

Plug these numbers back into the problem to see if they work.

 

Have fun.

 

Dan