Bill drove from Ajax to Bixby at an average speed of 50mi/h. On the way back, he drove at 60mi/h. The total trip took 4 2/3 hours of driving time. Find the distance between the two cities.
Let the distance between the two cities be d.
The time it took for Bill to drive from Ajax to Bixby is d/50.
The time it took for Bill to drive from Bixby back to Ajax is d/60.
The total driving time is d/50 + d/60.
The total driving time in hours is 4 2/3 = 14/3 hours.
So, d/50 + d/60 = 14/3.
To get rid of the denominators, we can multiply each term by 150 (the LCM of 50 and 60).
3d + 2d = 14 * 50.
5d = 700.
Thus, the distance between the two cities is d = 700/5 = <<700/5=140>>140 miles. Answer: \boxed{140}.
To find the distance between the two cities, we need to use the formula: distance = speed * time.
Let's denote the distance between Ajax and Bixby as "d".
During the first part of the trip, Bill drove at an average speed of 50 mi/h. Let's denote the time he spent on this part as "t1". The distance covered during this part can be calculated as d = 50 * t1.
During the second part of the trip, Bill drove at an average speed of 60 mi/h. Let's denote the time he spent on this part as "t2". The distance covered during this part can be calculated as d = 60 * t2.
According to the problem, the total driving time is 4 2/3 hours, which can be written as 14/3 hours. Therefore, we have the equation t1 + t2 = 14/3.
We also know that the total distance is the same for both parts of the trip. Therefore, we have the equation 50 * t1 = 60 * t2.
To solve these equations, we can use substitution.
From the second equation, we can express t1 in terms of t2:
t1 = (60 * t2) / 50
t1 = (6/5) * t2
Substituting this into the first equation:
(6/5) * t2 + t2 = 14/3
(16/5) * t2 = 14/3
Multiply both sides by 5/16 to isolate t2:
t2 = (14/3) * (5/16)
t2 = 35/12
Now we can calculate t1:
t1 = (6/5) * (35/12)
t1 = 7/2
Finally, we can find the distance "d":
d = 50 * t1
d = 50 * (7/2)
d = 350/2
d = 175
Therefore, the distance between Ajax and Bixby is 175 miles.
To find the distance between the two cities, we can use the formula:
Distance = Speed * Time
Let's calculate the time it took for Bill to drive to Bixby using the given average speed of 50 mi/h.
Time = Distance / Speed
Time = (Distance to Bixby) / 50
Similarly, let's calculate the time it took for Bill to drive back from Bixby using the average speed of 60 mi/h.
Time = (Distance from Bixby) / 60
We are given that the total trip took 4 2/3 hours of driving time. Therefore, the total time for the trip is:
Total Time = Time to Bixby + Time from Bixby
4 2/3 = (Distance to Bixby) / 50 + (Distance from Bixby) / 60
Now, we need to solve this equation to find the distances. To do that, let's convert the mixed number to an improper fraction:
4 2/3 = (14/3)
Substituting it back into the equation:
14/3 = (Distance to Bixby) / 50 + (Distance from Bixby) / 60
To simplify the equation and get rid of the fractions, we can multiply through by the least common multiple (LCM) of the denominators, which is 150:
150 * (14/3) = 150 * ((Distance to Bixby) / 50) + 150 * ((Distance from Bixby) / 60)
Now, let's simplify:
700 = 3 * (Distance to Bixby) + 5 * (Distance from Bixby)
We have two unknowns, the distances to and from Bixby. To find them, we need an additional equation. We can use the fact that the total distance of the trip is the same as the sum of the distances to and from Bixby.
Let's call the distance to Bixby "x" and the distance from Bixby "y." So we have:
Distance to Bixby + Distance from Bixby = Total Distance
Plugging in the given values, we get:
x + y = Total Distance
Since we can't solve these two equations with two unknowns uniquely, we need another equation. Unfortunately, the information provided doesn't give us any additional insight or a direct equation for the distances.
Therefore, we can't find the distance between the two cities with the given information.