Please explain to me how to solve this problem!! Thank you

Question

, two coast guard cutters are 225 miles apart traveling toward each other, one from the east and the other from the west. searching for a disabled boat. the eastbound cutter travels 5 miles per hour faster than the westbound cutter. If the two cutters pass each other after 3 hours, find the average speed of each cutter.

Answer 1

Let the two speeds be v for the westbound cutter, and v + 5 for the eastbound cutter.

 

d = initial separation distance = 225 miles

t = time they meet = 3 hours

 

Use the formula: distance = speed * time

 

The eastbound cutter travels a distance (v + 5)t = (v + 5)*(3).  During the same 3 hours, the westbound cutter travels a distance vt = v*(3).  The sum of the travel distances of the two cutters must equal their initial separation distance, so

 

d = 3(v + 5) + 3v

 

225 = 3(v + 5) + 3v

 

225 = 6v + 15

 

v = (225 - 15) / 6   = 35

 

v + 5 = 35 + 5 = 40

 

Speed of eastbound cutter is 40 mph

Speed of westbound cutter is 35 mph