Question

LE 5

Try It! Solve Work and Time Problems
5. 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 min. 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

3.103 miles

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:

`(x)/(12)+1.5+(x)/(2.5)=3\\(x)/(12)+(x)/(2.5)=1.5\\(x(2.5)+x(12))/(12*2.5)=1.5\\(2.5x+12x)/(30)=1.5\\14.5x=30*1.5\\14.5x=45\\x=(45)/(14.5)\\x=3.103`

THus, the distance is 3.103 miles