Distance rate and time

Question

Sally left the city for vacation. Dan left 8 hours later going 40 mph faster to catch up. After 7 hours Dan caught up. What was Sally's average speed?

Answer 1

Sally travels for a total of 15 hours before Dan catches up, if we let her speed = x ,we can model her position by the equation:

S = 15x

Because Dan only travels 7 hours before catching up to Sally, and it is stated that he travels 40 mph faster, we can model his position with the equation:

D = 7(x + 40)

Because it is given that Dan caught up we can assume their positions are equal and use that knowledge to solve for Sally’s speed, x.

S = D

15x = 7(x + 40)

15x = 7x + 280

8x = 280

x = 35

ANSWER: Sally’s average speed is 35 mph.

Answer 2

Distance = (Rate)(Time)

Let x = Sally's speed. Then x + 40 =

Dan's speed

15x = 7(x+40)

8x = 280

x = 35 mph