How do you find both speed rates

Question

Beth can travel 208 miles I the same length of time it takes Anna to travel 192 miles. If Beth's speeds is 3mph greater than Anna's, find both rates

Answer 1

v = Beth's speed

u = Anna's speed

 

speed = distance / time

 

Given data:

 

v = 208/t

u = 192/t

v = u + 3

 

Then

 

208/t = 192/t + 3

 

Solve for t to get v and u.  Multiply both sides by t and get

 

208 = 192 + 3t ⇒ t = (208 - 192) / 3 = 5.33 hours

 

Then

 

v = 208/5.33 mph = 39.02 mph

u = 192/5.33 mph = 36.02 mph