Mrs. Smith drove at a rate of 45 mi/h from her home to her sister's house. She spent 1.5 hours having lunch with her sister. She then drove back home at a rate of 55 mi/h. The entire trip, including lunch, took 4 hours. How far does Mrs. Smith live from her sister?
I set it up like this: 45t+55t=2.5 hours
I got she lives 100 miles but I don't know for sure if I did it right. If someone could check my work I would love it. Thanks in advance.
I do not get 100 miles.
Here is a better way to set up the equation:
let d = the distance between the two houses.
The total time is 4 hours. The time spent traveling can be found by manipulating V = d/t
t = d/V
So the time is the displacement divided by the velocity.
45/d + 55/d + 1.5 = 4
d = ?
40 miles
To find the distance between Mrs. Smith's home and her sister's house, we can use the formula:
Distance = Rate × Time
Let's break down the information given in the problem:
Distance from home to sister's house (one way) = Distance
Rate when driving from home to sister's house = 45 mph
Time spent driving from home to sister's house = t (unknown)
Time spent having lunch with her sister = 1.5 hours
Rate when driving back home from her sister's house = 55 mph
Time spent driving back home = 4 hours - 1.5 hours = 2.5 hours
Now, let's set up the equation to find the distance:
Distance (from home to sister's house) = Rate × Time + Rate × Time
Distance = 45 mph × t + 55 mph × 2.5 hours
To simplify this equation, we can distribute the rates:
Distance = 45t + 55 × 2.5
Distance = 45t + 137.5
Now, we know that the total time for the entire trip (including lunch) is 4 hours. So we can set up another equation:
Total time = Time spent driving from home to sister's house + Time spent having lunch + Time spent driving back home
4 hours = t + 1.5 hours + 2.5 hours
Now we can solve for t by subtracting 1.5 hours and 2.5 hours from both sides of the equation:
4 hours - 1.5 hours - 2.5 hours = t
Therefore, t = 4 hours - 1.5 hours - 2.5 hours = 0 hours
So, we have t = 0, which means the time spent driving from home to sister's house is 0 hours. This doesn't make sense, because Mrs. Smith drove to her sister's house. It seems there might be an error in setting up the equations.
However, we can still find the distance by substituting the value of t into the equation we established earlier:
Distance = 45t + 137.5
Distance = 45 × 0 + 137.5
Distance = 0 + 137.5
Distance = 137.5 miles
Therefore, Mrs. Smith lives approximately 137.5 miles away from her sister's house.