Wilma drove at an average speed of 35 mi/h from her home in City A to visit her sister in City B. She stayed in City B 15 hours, and on the trip back averaged 40 mi/h. She returned home 41 hours after leaving. How many miles is City A from City B?
distance between two towns --- x miles
time for first trip = x/35
time for 2nd trip = x/40
x/35 + x/40 + 15 = 41
LCD = 280
8x + 7x = 7280
x = 485 1/3 miles
To find the distance between City A and City B, we need to determine the travel time for each leg of the trip.
Let's first calculate the travel time for the trip from City A to City B.
We know that Wilma's average speed for this leg of the trip was 35 mi/h, and the total travel time is the time spent driving plus the time spent in City B.
Let's represent the time spent driving as x (in hours). The time spent in City B is given as 15 hours.
Therefore, the total travel time from City A to City B is:
x + 15 hours
Next, let's calculate the travel time for the trip from City B back to City A.
Wilma's average speed for this leg of the trip was 40 mi/h, and the total travel time is the time spent driving plus the time spent in City B.
The time spent driving for the return trip is also x (in hours), and the total travel time is given as 41 hours.
Therefore, the total travel time from City B back to City A is:
x + 15 + x = 41
2x + 15 = 41
2x = 41 - 15
2x = 26
x = 26/2
x = 13 hours
Now that we know the value of x, which represents the time spent driving for both legs of the trip, we can calculate the distance.
The distance between City A and City B is the same for both legs of the trip, and it can be calculated using the formula:
Distance = Speed x Time
For the trip from City A to City B:
Distance = 35 mi/h x 13 hours
And for the return trip from City B to City A:
Distance = 40 mi/h x 13 hours
Both calculations will give us the same distance since it is the same road traveled.
Therefore, the distance between City A and City B is:
Distance = 35 mi/h x 13 hours = 455 miles
To determine the distance between City A and City B, we need to use the formula: distance = speed × time.
First, let's calculate the time it took Wilma to drive from City A to City B. We can use the formula: time = distance / speed.
Let's assume the distance between the two cities is "d" miles.
So, the time taken to drive from City A to City B is: time1 = d / 35 mi/h.
After reaching City B, Wilma stayed for 15 hours.
The time taken for the return trip from City B to City A is: time2 = d / 40 mi/h.
Finally, we know that the total time for the round trip was 41 hours. Therefore, the equation can be written as:
(time1 + 15 hours + time2) = 41 hours.
Substituting the previously calculated values, we have:
(d / 35 mi/h + 15 hours + d / 40 mi/h) = 41 hours.
Now, we can solve this equation to find the value of d, the distance between City A and City B.
To simplify the equation, we need to find a common denominator for the fractions. The least common multiple (LCM) of 35 and 40 is 280. So, let's rewrite the equation:
(8d / 280 + 15 hours + 7d / 280) = 41 hours.
Combining the fractions, we have:
(15 hours + 8d + 7d) / 280 = 41 hours.
Combining like terms, we get:
(15 hours + 15d) / 280 = 41 hours.
Now, we can cross multiply and solve for d:
15 hours + 15d = 41 hours * 280.
15d = 11480 hours - 15 hours.
15d = 11465 hours.
Dividing both sides by 15:
d = 764.33 miles.
Therefore, City A is approximately 764.33 miles away from City B.