at the beginning of a walk Roberto and juanita are 6.6 miles apart. If they leave at the same time and walk in the same direction Roberto overtakes Juanita in 11 hrs. If they walk towards each other they meet in one hour what are their speeds

Hi Mishonta;

(R+J)=(6.6 miles)/(1 hour)

Roberto is the faster walker with the longer distance...

R=[(6.6+x) miles]/(11 hours)

J=(x miles)/(11 hours)

R+J=R+J

[((6.6+x) miles)/(11 hours)]+[(x miles)/(11 hours)]=(6.6 miles)/(1 hour)

Let's multiply the right side of the equation by 11/11

[((6.6+x) miles)/(11 hours)]+[(x miles)/(11 hours)]=[(6.6 miles)/(1 hour)](11/11)

[((6.6+x) miles)/(11 hours)]+[(x miles)/(11 hours)]=(72.6 miles)/(11 hours)

The denominators are all 11 hours. These cancel...

[((6.6+x) miles)/(11 hours)]+[(x miles)/(11 hours)]=(72.6 miles)/(11 hours)

[(6.6+x) miles]+(x miles)=72.6 miles

The unit of miles is in the numerator of both sides of the equation. It cancels...

[(6.6+x) miles]+(x
miles)=72.6 miles

6.6+x+x=72.6

2x+6.6=72.6

2x=66

x=33

**Juanita's speed is (33 miles)/(11 hours)=3 miles/hour**

**Roberto's speed is [(33+6.6)miles]/(11 hours)=3.6 miles/hour**