A car travels 30 miles in the same time that a car traveling 5 miles per hours faster travels 45 miles. What is the rate of each car?
speed of slower car --- x
speed of faster car ---- x+5
time of slower car to go 30 miles = 30/x
time of faster car to go 45 miles = 45/(x+5)
but they are the same, so ---
45/(x+5) = 30/x
45x = 30x + 150
15x = 150
x = 10
so the slow car goes 10 mph (very slow) and the faster car goes 15 mph
check:
at 10 mph, it takes 30/10 or 3 hrs to got 30 miles.
at 15 mph , to go 45 miles, takes 45/15 = 3 hrs
To solve this problem, we can use two key formulas: Distance = Speed × Time and Time = Distance / Speed.
Let's assume the rate of the slower car is "r" miles per hour. This means the speed of the slower car is r mph.
We are given that the slower car travels 30 miles in the same time it takes for the faster car to travel 45 miles.
Using the formula Distance = Speed × Time, we can set up the following equation for the slower car:
30 = r × Time ----- (Equation 1)
Now, let's find the rate of the faster car. We are told that it travels 5 miles per hour faster than the slower car. So the rate of the faster car is r + 5 mph.
Using the formula Distance = Speed × Time, we can set up the following equation for the faster car:
45 = (r + 5) × Time ----- (Equation 2)
Since both cars are traveling for the same amount of time, we can express Time in terms of Distance and Speed using the formula Time = Distance / Speed.
From Equation 1: Time = 30 / r
From Equation 2: Time = 45 / (r + 5)
Since these two expressions are equal, we can set them equal to each other:
30 / r = 45 / (r + 5)
To solve for r, we can cross-multiply and solve the resulting equation.
30(r + 5) = 45r
30r + 150 = 45r
150 = 15r
Dividing both sides of the equation by 15, we get:
r = 10
Therefore, the rate of the slower car is 10 mph, and the rate of the faster car is 10 + 5 = 15 mph.