At 9:00 Mary Thorne set out from her house for a picnic, traveling at 15 km/h on her bike. her sister lifet 15 min later and traveled at the speed of 30 km/h. If both her sisters arrived at the picnic area at the same time, how far did each travel?
How would I set this problem up?
To set up this problem, you should first determine the time it took for Mary Thorne to reach the picnic area. Since Mary started at 9:00 and her sister started 15 minutes later, Mary had a head start of 15 minutes, which is equivalent to 15/60 = 0.25 hours.
Let's assume it took t hours for both Mary and her sister to reach the picnic area.
Based on the given information, Mary traveled at a speed of 15 km/h for t + 0.25 hours, and her sister traveled at a speed of 30 km/h for t hours to meet at the picnic area.
The distance traveled by each person is given by the formula:
Distance = Speed x Time
For Mary: DistanceMary = 15 km/h x (t + 0.25) hours
For her sister: DistanceSister = 30 km/h x t hours
To find the distance traveled by each person, you can substitute the given speeds and times into the respective distance formulas.
To set up this problem, you can use the formula:
Distance = Speed * Time
Let's define some variables to represent the unknown distances. Let D1 be the distance traveled by Mary Thorne, and D2 be the distance traveled by her sister.
Now, let's use the information provided in the problem:
1. Mary Thorne's speed is 15 km/h, and her sister's speed is 30 km/h.
2. Mary Thorne started 15 minutes earlier than her sister.
Since we want to find the distances traveled by each of them, we can write two equations using the formula above:
1. For Mary Thorne: D1 = 15 km/h * T, where T is the time she traveled.
2. For her sister: D2 = 30 km/h * (T - 15/60), where T - 15/60 represents the time her sister traveled after Mary Thorne.
We subtract 15/60 from T because Mary Thorne started 15 minutes earlier.
Since both of them arrived at the picnic area at the same time, we can set the distances equal to each other:
D1 = D2
Now, you have a system of equations that can be solved to find the distances traveled by each of them.
didn't they both travel the same distance?
let that distance be x km
so mary's time = x/15
sister's time = x/30
The difference is their times is equal to 1/4 hour.
Translate that into an equation and solve for x
Well, it seems like Mary and her sister are having a race to the picnic area! To set up the problem, we need to figure out the time it took for each sister to reach the picnic area.
Let's start with Mary. We know she traveled at 15 km/h and left her house at 9:00. So, the time Mary spent biking can be represented as:
Time = Distance / Speed
Since we don't know the distance yet, let's call it 'd'. Therefore, the time it took Mary can be written as:
Time₁ = d / 15
Now, for her sister who left 15 minutes later. We need to find out how long she spent biking too. Since she traveled at 30 km/h, her time can be represented as:
Time₂ = d / 30
Since both sisters arrived at the same time, we can equate their times:
Time₁ = Time₂
Now, it's time for some math wizardry to solve this equation! After we solve for 'd', we'll know the distance traveled by each sister.
Let's grab our calculators and start crunching those numbers!