Destiny and Alicia both leave the coffee shop at the same time, but in opposite directions. If Alicia travels 4 mph faster than Destiny and after 3 hours they are 78 miles apart, how fast is each traveling?

Answer: Destiny's speed is 11 mph.

Alicia's speed is 15 mph

Step-by-step explanation:

Destiny and Alicia both leave the coffee shop at the same time, but in opposite directions. If they are 78 miles apart after 3 hours, it means that the total distance that they covered in 3hours is 78 miles

Let x represent the speed at which Destiny travelled. If Alicia travels 4 mph faster than Destiny, it means that the speed at which Alicia travelled is (x + 4) mph

Distance = speed * time

Distance covered by Destiny in 3 hours is

3 * x = 3x

Distance covered by Alicia in 3 hours is

3 (x + 4) = 3x + 12

Since the total distance is 78 miles, then

3x + 3x + 12 = 78

6x = 78 - 12 = 66

x = 66/6 = 11 mph

Alicia's speed is

11 + 4 = 15 mph