Find the rate of each hiker

Two hikers are 77 miles apart and walking toward each other. They meet in 10 hours. Find the rate of each
hiker if one hiker walks 3.3 mph faster than the other.

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This is a distance, rate, time problem.

Distance = rate x time

One hiker
distance = d
rate = r 
time = 10  {they meet in 10 hours}
d = 10r  {distance = rate x time}

Other hiker
distance = d
rate = r + 3.3  {one hiker walks 3.3 mph faster than the other}
time = 10  {they meet in 10 hours}
d = 10(r + 3.3)  {distance = rate x time}
d = 10r + 33  {used distributive property}

They are 77 miles apart and walking toward each other.  Therefore, their combined distances will equal 77.

10r + 10r + 33 = 77   {added distances together and set equal to 77}
20r + 33 = 77  {combined like terms}
20r = 44  {subtracted 33 from each side}
r = 2.2  {divided each side by 20}
r + 3.3 = 5.5  {substituted 2.2, in for r, into r + 3.3}

The rate of one hiker is 2.2 mph
The rate of the other hiker is 5.5 mph

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