Answer:
The speed of the first car is 60 mph
Step-by-step explanation:
speed = distance/time
Solve the above equation for distance to get
distance = speed * time
or simply
d = st
Now we use this formula for distance to write an equation for each car.
Let s = speed of second car
Then since the speed of the first car is 10 mph faster, the first car's speed is s + 10.
The time the two cars traveled is equal but unknown, so let the time = t.
First car: speed = s + 10; time = t; distance = 120 miles
d = st
120 = (s + 10)t
(s + 10)t = 120 Equation 1
Second car: speed = s; time = t; 100 miles
d = st
100 = st
st = 100 Equation 2
Equations 1 and 2 form a system of 2 equations in 2 unknowns.
(s + 10)t = 120
st = 100
Distribute t in the first equation.
st + 10t = 120
From the second equation we know st = 100, so substitute 100 for st.
100 + 10t = 120
10t = 120
t = 2
The time traveled was 2 hours.
Equation 2:
st = 100
Substitute t with 2.
s * 2 = 100
s = 50
The speed of the second car was 50 mph.
The speed of the first car is s + 10.
s + 10 = 50 + 10 = 60
Answer: The speed of the first car is 60 mph
