Hi

If car B travels 10 mph faster than car A speed 

& Car A travels 120 miles in the same time that car B travels 150 miles

Note:  D = rt   0r t = D/rate

Question states***

   ***  |Cross Multiplying to solve

  120(x+10) = 150x

   1200 = 30x

     x = 40mph, speed of car A.  Car B speed is 50mph

CHECKING our answer***

 = 3hr

Wish You the Best in your Studies.





 

Answer by ptaylor(2198)   (Show Source): You can put this solution on YOUR website!
 Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r

Let r=car A's rate

Then r+10=car B's rate



Time travelled by car A=120/r

Time travelled by car B=150/(r+10)

Now we are told that these times are the same, soooo:

120/r=150/(r+10) multiply each side by r(r+10)

120(r+10)=150r simplify

120r+1200=150rsubtract 120r from each side

120r-120r+1200=150r-120r

30r=1200

r=40mph---Car A speed

r+10=40+10=50 mph -----Car B's speed (or rate)

CK

120/40=150/50

3=3



Hope this helps--ptaylor 

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
 the general equation to use is:

RT = D

this equations means:

rate * time = distance.





car A travels 120 miles in the same time that car B travels 150 miles.

If car B travels 10 mph faster than car A, how fast is each car travelling.





since they both travel for the same amount of time, we'll let T represent the amount of time it takes in hours.





If we allow the rate of car A to be equal to R, then the rate of car B will have to be R + 10 because car B travels 10 miles per hour faster than car A.





the equation for car A becomes:





R * T = 120





the equation for car B becomes:





(R + 10) * T = 150





these are 2 equations that need to be solved simultaneously in order to find the same answer that is applicable to both.





those equations are:

R * T = 120

(R + 10) * T = 150





we'll solve by substitution.





in the equation of R * T = 120, solve for T to get:

T = 120 / R





in the equation of (R + 10) * T = 150, replace T with 120 / R to get:

(R + 10) * 120 / R = 150





solve for R in this equation as follows:

start with:

(R + 10) * 120 / R = 150

multiply both sides of this equation by R to get:

(R + 10) * 120 = 150 * R

simplify to get:

120 * R + 1200 = 150 * R

subtract 120 * R from both sides of this equation to get:

1200 = 150 * R - 120 * R

simplify to get:

1200 = 30 * R

divide both sides of this equation by 30 to get:

40 = R





since R = 40, then R + 10 must be equal to 50.





car A is traveling at 40 miles per hour.

car B is traveling at 50 miles per hour.

those are your answers.





we'll use those values for R in the original equations to see if they make sense.





in the first equation, we have:

R * T = 120

since R = 40, this equation becomes:

40 * T = 120

divide both sides of this equation by 40 and you get:

T = 3





in the second equation, we have:

(R + 10) * T = 150

since R = 40, thyis equation becomes:

(40 + 10) * T = 150

simplify to get:

50 * T = 150

divide both sides of this equation by 50 to get:

T = 3





both cars travel for the same time.

car B is traveling 10 miles per hour faster than car A.

everything checks out, so the solution is:





car A is traveling at 40 miles per hour.

car B is traveling at 50 miles per hour.





extra information:

they are both traveling for 3 hours each.















 

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