Rates Quesion

Question

Kent drives his Mazda 552 miles in the same time that it takes Dave to drive his Nissan 480 miles. If Kent averages 9 miles per hour faster than Dave, find their rates.

Answer 1

distance=rate*time

d=rt

552=(r+9)t for Kent

480=rt for Dave

552/(r+9)=t

480/r=t

552/(r+9)=480/r

cross multiply

552r=480(r+9)

552r=480r+4320

552r-480r=4320

72r=4320

r=4320/72

r=60 mph

r+9=69 mph

Answer 2

Hi Connor,

 

Here is how to solve it:

 

First, define what speed is:  speed = d/t.

 

 

Let's set it up.

 

 

Kent speed = 552 miles             Dave's speed = 480 miles

                          t                                                 t

 

Since both have traveled same amount of time, both t are equal.

 

So,  552 miles      = t =     480 miles

      Kent speed                Dave's speed

 

Therefore,  552 miles   =    480 miles

                Kent speed       Dave's speed

 

Rewrite the equation in terms of Dave's speed

 

 552 miles    =    480 miles

Dave's + 9        Dave's speed    

 

From here, all you have to do is "cross-multiply."  Let's write Dave's as D.

 

552 miles   =   480 miles

   D + 9                D

 

552 D = 480 (D + 9)

 

552 D = 480 D + 4320

 

72 D = 4320   

 

D = 60

 

But how many hours? 480 miles/60 MPH

(since both drivers drove same amount of time) = 8 hrs.

 

So, Dave's speed was 60 MPH & Kent speed was 69 MPH.  Let's check it.

 

60 * 8 = 480 for Dave &  69 * 8 = 552 for Kent.  And yes, it does check out as both drove for same amount of time (8 hrs) and Dave with 60 MPH and Kent with 69 MPH, respectively.

 

There you have it.  Good luck. 

 

      

Answer 3

Let x be Dave's speed

 

so, (x + 9) is Kent's speed

 

(x + 9)t = 552               eq. 1

 

xt = 480   ---------> t = 480/x                  

 

let's plug t in to eq. 1

 

(x + 9)(480/x) = 552

 

480 + 4320/x = 552

 

4320/x = 552 - 480

 

4320/x = 72

 

4320 = 72x

 

x = 60

 

so, Dave's speed is 60 mph and Kent's speed is 69 mph