Latanya leaves her house at 12: 30 p. m. and bikes at 12 mi/h 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. how far is marta's house from latanya's house?

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 ,

  the time from Marta's house to her house is

∵ Latanya bikes at 12 mi/h to Marta's house

∵ Distance = speed × time

∴ d = 12 ×

∵ Both girls walk back to latanya's house at 2.5 mi/h

∴ d = 2.5 ×

- Equate the two expressions of d

∴ 12 = 2.5 ⇒ (1)

∵ + = 1.5

- Subtract from both sides

∴ = 1.5 - ⇒ (2)

- Substitute equation (2) in equation (1)

∴ 12 = 2.5(1.5 - )

∴ 12 = 3.75 - 2.5

- Add 2.5 to both sides

∴ 14.5 = 3.75

- Divide both sides by 14.5

∴ = hour

∴ She spends 15/58 hour to bike to Marta's house

- Lets find d

∵ d = 12

∴ d = miles

* Marta's house is 3.10 miles from Latanya's house

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