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 50 mi/h. She returned home 41 hours after leaving. How many miles is City A from City B
Distance = Speed * Time
D= 35 * T
D= (41-15) * 50
26*50T=1300T
Please help, Im not sure where I went wrong.
better to use time = distance/speed, since we are adding up times here.
d/35 + 15 + d/50 = 41
17/350 d = 26
d = 26 * 350/17
d = 9100/17 = 535.29
check:
535.29/35 = 15.294
535.29/50 = 10.706
total driving time is 26 hours, as expected.
To find the distance between City A and City B, we need to calculate the distance of each leg of the trip separately and then add them together.
Let's start with the first leg, from City A to City B.
We are given that Wilma drove at an average speed of 35 mi/h. We can use the formula D = S * T, where D is the distance, S is the speed, and T is the time. In this case, we want to find the distance, so we rearrange the formula to D = 35 * T.
Since we don't know the time it took for Wilma to travel from City A to City B, let's call it T1.
So the distance from City A to City B is D1 = 35 * T1.
Next, let's calculate the distance of the second leg, from City B to City A.
We are given that Wilma drove at an average speed of 50 mi/h. Using the same formula, D = S * T, we can find the distance of this leg. Let's call the time it took for Wilma to travel from City B to City A T2.
So the distance from City B to City A is D2 = 50 * T2.
Now, we know that Wilma stayed in City B for 15 hours. We also know that she returned home 41 hours after leaving. So the total time for the round trip is T1 + 15 + T2 = 41.
We can rearrange this equation to T1 + T2 = 41 - 15, which simplifies to T1 + T2 = 26.
Now, we have a system of two equations:
D1 = 35 * T1
D2 = 50 * T2
T1 + T2 = 26
We need to solve this system of equations to find both T1 and T2. Then we can calculate the total distance by adding the distances from each leg.
It seems that you made a mistake when calculating the distance for the first leg. Instead of D1 = 35 * T, you calculated D1 as (41-15) * 50, which is not correct. Please try correcting the calculation and continue from there.
To find the distance between City A and City B, we need to find the total distance traveled on the trip back and subtract the distance traveled during the 15-hour stay in City B.
Let's break down the steps:
1. Find the distance traveled on the trip back:
Distance = Speed * Time
D = 50 * (41 - 15) [41 hours - 15 hours = 26 hours]
D = 50 * 26
D = 1300 miles
2. Find the total distance traveled during the entire trip:
Total Distance = Distance on trip back + Distance during stay in City B
Total Distance = 1300 miles + Distance during stay in City B
3. Since the average speed on the way to City B is not given, we need to find the time taken for the trip to City B using the given information.
Time = Distance / Speed
35 = Distance / Time to City B
Time to City B = Distance / 35
4. Substitute the value of Time to City B back into the equation for total distance:
Total Distance = 1300 miles + (Distance / 35) * 35
Total Distance = 1300 miles + Distance
5. Now, we can solve for the Distance between City A and City B:
Total Distance = Distance between City A and City B
Distance between City A and City B = Total Distance - 1300 miles
Therefore, the distance between City A and City B is equal to the Total Distance minus 1300 miles.