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sergiy2304 [10]
3 years ago
14

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 gir

ls 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?
Mathematics
1 answer:
Llana [10]3 years ago
6 0

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 t_{1},

  the time from Marta's house to her house is t_{2}

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

∵ Distance = speed × time

∴ d = 12 × t_{1}

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

∴ d = 2.5 × t_{2}

- Equate the two expressions of d

∴ 12 t_{1} = 2.5 t_{2} ⇒ (1)

∵ t_{1} + t_{2} = 1.5

- Subtract t_{1} from both sides

∴ t_{2} = 1.5 - t_{1} ⇒ (2)

- Substitute equation (2) in equation (1)

∴ 12 t_{1} = 2.5(1.5 - t_{1})

∴ 12 t_{1} = 3.75 - 2.5t_{1}

- Add 2.5 t_{1} to both sides

∴ 14.5 t_{1} = 3.75

- Divide both sides by 14.5

∴ t_{1} = \frac{15}{58} hour

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

- Lets find d

∵ d = 12 t_{1}

∴ d = 12*\frac{15}{58}=3.10 miles

* <em>Marta's house is 3.10 miles from Latanya's house</em>

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