Answer:
Marta's house is 3.10 miles from Latanya's house
Step-by-step explanation:
* Lets explain how to solve the problem
- Latanya leaves her house at 12:30 p.M.
- She bikes at 12 mi/hr to Marta's house
- She stays at Marta's house for 90 minute
- Both girls walk back to latanya's house at 2.5 mi/h
- They arrive at latanya's house at 3:30 p.M.
- We need to know how far is Marta's house from latanya's house
∵ Latanya starts her trip at 12:30 p.M.
∵ She returns her home at 3:30 p.M.
∴ The time of her trip is  → 3:30 - 12:30 = 3 hours
- But she stays at at Marta's house for 90 minutes
∵ 1 hour = 60 minutes
∴ 90 minutes = 90 ÷ 60 = 1.5 hours
∴ The time from her house to Marta's house and from Marta's house
  to her house is → 3 - 1.5 = 1.5 hours
- Assume that the distance from her house to Marta's house is d
 and the time from her house to Marta's house is [tex]t_{1}[/tex],
 the time from Marta's house to her house is [tex]t_{2}[/tex]
∵ Latanya bikes at 12 mi/h to Marta's house
∵ Distance = speed × time
∴ d = 12 × [tex]t_{1}[/tex]
∵ Both girls walk back to latanya's house at 2.5 mi/h
∴ d = 2.5 × [tex]t_{2}[/tex]
- Equate the two expressions of d
∴ 12 [tex]t_{1}[/tex] = 2.5 [tex]t_{2}[/tex] ⇒ (1)
∵ [tex]t_{1}[/tex] + [tex]t_{2}[/tex] = 1.5
- Subtract [tex]t_{1}[/tex] from both sides
∴ [tex]t_{2}[/tex] = 1.5 - [tex]t_{1}[/tex] ⇒ (2)
- Substitute equation (2) in equation (1)
∴ 12 [tex]t_{1}[/tex] = 2.5(1.5 - [tex]t_{1}[/tex])
∴ 12 [tex]t_{1}[/tex] = 3.75 - 2.5[tex]t_{1}[/tex]
- Add 2.5 [tex]t_{1}[/tex] to both sides
∴ 14.5 [tex]t_{1}[/tex] = 3.75
- Divide both sides by 14.5
∴ [tex]t_{1}[/tex] = [tex]\frac{15}{58}[/tex] hour
∴ She spends 15/58 hour to bike to Marta's house
- Lets find d
∵ d = 12 [tex]t_{1}[/tex]
∴ d = [tex]12*\frac{15}{58}=3.10[/tex] miles
* Marta's house is 3.10 miles from Latanya's house
Answer:
Marta's house is 3.10 miles from Latanya's house
Step-by-step explanation:
