Question

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?

Answer 1

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 - 2.5$t_{1}$

- 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

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