Dan's speed is 60 miles per hour.
First, we know that Kay drives at 45 miles per hour for 20 minutes to arrive at her work, so the distance between her home and work is:
D = speed*time.
Where:
speed = 45 mi/h
time = 20 min.
First, we need to write the time in hours, so we get:
60 min = 1 hour.
20 min = 1/3 hours.
Then the distance will be given by:
D = (45 mi/h)*(1/3 h) = 15 mi
The distance is 15 miles.
Now, we know that Dan takes 2 minutes less than Kay to drive the same distance, then Kay's equation is:
S*(18 min) = 15 mi
Writing 18 min in hours we get:
18 min = (18/60) hours = 0.3 hours.
Then:
S*(0.3 h) = 15 mi
S = 15mi/0.3 h = 60 mi/h.
Dan's speed is 60 miles per hour.
If you want to learn more about speed:
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