Answer:
Original speed = 32 km/h
First car's new speed = 33 km/h
Second car's new speed = 22 km/h
Step-by-step explanation:
"two cars are traveling down the highway with the same speed"
Let the original speed of both cars be x.
"the first car increases its speed by 1 km per hour"
Now its speed is x + 1.
"the other car decreases its speed by 10 km per hour"
Now its speed is x - 10.
Now we need a relationship between speed, distance, and speed.
speed = distance/time
Multiply both sides by time and switch sides.
distance = speed * time
In 2 hours, the first car covers (speed * time for first car):
distance = 2 * (x + 1)
In 3 hours, the second car covers (speed * time for second car)
distance = 3 * (x - 10)
The distances are equal, so we set them equal and solve the equation for x.
2(x + 1) = 3(x - 10)
2x + 2 = 3x - 30
2 = x - 30
32 = x
x = 32
The original speed of the cars was 32 km/h
After the speeds changed, the first car's speed is
x + 1 = 32 + 1 = 33 km/h
The second car's speed becomes
x - 10 = 32 - 10 = 22 km/h
Let's check:
In 2 hours, the first car covers 2 h * 33 km/h = 66 km
In 3 hours, the second car covers 3 h * 22 km/h = 66 km
The distances are the same, so our answer is correct.
Answer:
50 mph
Step-by-step explanation:
3(s-10)=2(s+10)
3s-30=2s+20
s=50
