Question 838771
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.