Suppose that a cyclist began a 510 mi ride across a state at the western edge of the state at the same that a car traveling toward it leaves the eastern end of the state if the bicycle and car met after 8.5 hr and the car traveled 33.4 mph faster than the bicycle find average rate of each
Db + Dc = 510 mi.
Vb*t + Vc*t = 510.
Vb*t + (Vb+33.4)t = 510.
t = 8.5 hrs.
Vb = ?
Vc = Vb + 33.4.
To solve this problem, we can use the formula: Distance = Speed * Time. Let's denote the speed of the bicycle as "x" mph and the speed of the car as "x + 33.4" mph (since the car travels 33.4 mph faster than the bicycle).
We are given that the bicycle and car met after 8.5 hours, so the time for both of them would be 8.5 hours. Since the distance traveled is the same for both the bicycle and the car, we can set up the following equation:
Distance (bicycle) = Distance (car)
(x mph) * (8.5 hours) = (x + 33.4 mph) * (8.5 hours)
Now, we can solve this equation to find the value of x, which represents the speed of the bicycle. Let's simplify the equation:
8.5x = 8.5(x + 33.4)
8.5x = 8.5x + 284.9
By subtracting 8.5x from both sides, we get:
0 = 284.9
Uh-oh! We have encountered a problem. The equation simplifies to 0 = 284.9, which is not possible.
This means that there is no solution that satisfies the given conditions. It is not possible for the bicycle and the car to meet after 8.5 hours if the car is traveling 33.4 mph faster than the bicycle.
Therefore, we cannot determine the average rate of each since there is no valid solution.