Answer:
3.103 miles
Step-by-step explanation:
We know D = RT, where
D is distance
R is rate
T is time
Let distance of Latanya and Marta's house be "x".
THe first leg, the distance is x and rate is 12, so the time it takes is:
D = RT
T = D/R
T = x/12
Second leg is just staying in marta's house for 90 minutes, which is 1.5 hours
Third leg is when they cover same distance , x, but rate is 2.5, so time is:
T = D/R
T = x/2.5
Since the whole journey took 3 hours (12.30 - 3.30), we can simmply add them and equate to 3 and solve for x:
[tex]\frac{x}{12}+1.5+\frac{x}{2.5}=3\\\frac{x}{12}+\frac{x}{2.5}=1.5\\\frac{x(2.5)+x(12)}{12*2.5}=1.5\\\frac{2.5x+12x}{30}=1.5\\14.5x=30*1.5\\14.5x=45\\x=\frac{45}{14.5}\\x=3.103[/tex]
THus, the distance is 3.103 miles
