Latanya leaves her house at 12: 30pm and bikes at 12 mi/h to marta’s house she stays at marta’s house for 90mij both girls walk back to latanya’s house at 2.3mi/h . they arrive at latanya house at 3: 30pm how far is marat’s house from latanya house

2.9 mi

Step-by-step explanation:

The time difference t between 12.30pm and 3.30pm is 3h.

Let the distance to Marat's house be s.

The equation to calculate velocity v is given by:

v = distance / time.

Now you can write an equation for the time difference t and use the two velocities and the 90 min(= 1.5h) she stays:

3 = s/12 + 1.5 + s/2.3

Solve this equation for s:

(1/12 + 10/23)* s = 1.5

s = 2.9

Martha's house is at a distance of 2.895 miles from LA Tanya's house.

Let the distance between Martha and LA Tanya's house = d

Total time = (3:30 - 12:30)pm = 3 hours

Stay time = 90 minutes = 1.5 hours

Recall :

Time = distance / speed

Therefore,

Cycling time = d / 12

Walking time = d / 2.3

Total time could be defined as :

Cycling time + walking time + stay time

d/12 + d/2.3 + 1.5 = 3

d/12 + d/2.3 = 3 - 1.5

d/12 + d/2.3 = 1.5

Multiply the denominator by 10

d/120 + d/23 = 1.5/10

L.C.M of 120 and 23 = 2760

(23d + 120d) / 2760 = 1.5/10

143d/2760 = 1.5/10

Cross multiply

1430d = 4140

d = 4140 / 1430

d = 2.895 miles

Hence, the distance between Martha and LA Tanya's house is 2.895 miles.

Find a similar solution here : link

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.