how would i do this problem elina and teresa raced on their bikes to the library after school. they both left at 3:00 pm and bicycled along the same trail elina rode at the speed of 12 miles an hour and teresa rode at the speed of 9 mph. elina got there 15minutes before teresa at wat time did elina get to the library
Let x=distance from library
x/9-x/12 = 0.25 (15 minutes)
Solve for x.
To find out when Elina got to the library, we need to calculate the time it took for both Elina and Teresa to reach the library.
Step 1: Calculate the time taken by Teresa
Since both Elina and Teresa left at 3:00 pm, but Elina arrived 15 minutes earlier than Teresa, we know that Teresa takes 15 minutes longer to reach the library.
Step 2: Convert the time difference to hours
To convert the time difference to hours, we divide the 15 minutes by 60 (there are 60 minutes in an hour).
15 minutes ÷ 60 = 0.25 hours
Step 3: Calculate the distance traveled by both Elina and Teresa
Since distance = speed × time, we can calculate the distance traveled by Elina and Teresa using the formula.
Distance Elina = Speed Elina × Time Elina
Distance Elina = 12 mph × Time Elina
Distance Teresa = Speed Teresa × Time Teresa
Distance Teresa = 9 mph × (Time Elina + 0.25 hours)
Step 4: Set up the equation
Since Elina and Teresa traveled the same distance, we can equate their distances and solve for Time Elina.
12 mph × Time Elina = 9 mph × (Time Elina + 0.25 hours)
Step 5: Solve the equation
By solving the equation, we can find the Time Elina.
12 mph × Time Elina = 9 mph × Time Elina + (9 mph × 0.25 hours)
12 Time Elina = 9 Time Elina + 2.25
12 Time Elina - 9 Time Elina = 2.25
3 Time Elina = 2.25
Time Elina = 2.25 ÷ 3
Time Elina = 0.75 hours
Step 6: Convert the time to minutes and add it to the starting time
To find the actual time Elina arrived at the library, we need to convert the time from hours to minutes and add it to the starting time (3:00 pm).
0.75 hours × 60 minutes = 45 minutes
3:00 pm + 45 minutes = 3:45 pm
Therefore, Elina arrived at the library at 3:45 pm.