Two cars start from the same place at the same time. After two hours, one car has traveled 30% farther than the other. If one car's speed is 20mph larger than the other car's speed, what are the speeds of the cars? Solve algebraically
Let's assume that the speed of the slower car is x mph.
According to the given information, the speed of the faster car is 20 mph greater than the speed of the slower car, so the speed of the faster car is (x + 20) mph.
Distance travelled by the slower car in 2 hours = x * 2 = 2x miles
Distance travelled by the faster car in 2 hours = (x + 20) * 2 = 2x + 40 miles
We are given that the faster car has traveled 30% farther than the slower car, so we can set up the following equation:
2x + 40 = 1.3(2x)
To solve for x, we can simplify the equation step-by-step:
2x + 40 = 2.6x
40 = 2.6x - 2x
40 = 0.6x
Dividing both sides of the equation by 0.6:
40/0.6 = x
x = 66.67
Therefore, the speed of the slower car is approximately 66.67 mph.
To find the speed of the faster car:
Speed of faster car = x + 20 = 66.67 + 20 = 86.67 mph
So, the speed of the cars are approximately 66.67 mph and 86.67 mph.
To solve this problem algebraically, let's assume the speed of the slower car is "x" mph. Therefore, the speed of the faster car would be "x + 20" mph.
We know that after two hours, one car has traveled 30% farther than the other. To find this distance relationship, we can use the equation:
Distance = Speed × Time
For the slower car, the distance traveled after two hours would be:
Distance of slower car = x mph × 2 hours
For the faster car, the distance traveled after two hours would be:
Distance of faster car = (x + 20) mph × 2 hours
According to the problem, the distance of the faster car is 30% greater than the distance of the slower car. Mathematically, we can express this as:
Distance of faster car = Distance of slower car + 30% of Distance of slower car
Or, in equation form:
(x + 20) mph × 2 hours = x mph × 2 hours + 0.3 × (x mph × 2 hours)
Let's simplify this equation:
2(x + 20) = 2x + 0.6x
Simplifying further:
2x + 40 = 2x + 0.6x
2x - 2x + 40 = 0.6x
40 = 0.6x
Now solve for x by dividing both sides by 0.6:
40 / 0.6 = x
x ≈ 66.67 mph
So, the speed of the slower car is approximately 66.67 mph, and the speed of the faster car is approximately 86.67 mph.