Question 838771: 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?
Found 3 solutions by ewatrrr, ptaylor, Theo:
Answer by ewatrrr(24785)   (Show Source):
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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