Distance Word Problem

Question

Brianna is 207 miles away from Zoe. They are traveling towards each other. If Zoe travels 9 mph faster than Brianna and they meet after 9 hours, how fast was each traveling?

Answer 1

distance = rate*time, d= rt

 

If Briana travels x miles

Zoe travels 207-x miles

 

Briana travels r mph

Zoe travels r+9 mph

 

Time = 9 hours

 

Plugging both into the distance formula:

Brianna: x = 9r

Zoe:     207-x = 9(r+9)

 

Substitute 9r in place of x in 2nd equation to solve for r

 

207-9r = 9r+81

207-81 = 18r

126 = 18r

r = 7 mph

 

Brianna travels at 7 mph

Zoe travels at 7+9 = 16 mph

 

Check Answer:

Together they should travel 207 miles

Zoe: 9(7) = 63 miles

Brianna:  9(16) = 144

Zoe + Brianna = 207 miles