Question

At the end of spring break, lucy left the beach and drove back towards home, driving at a rate of 40 mph. lucy's friend left the beach for home 30 minutes (half an hour) later, and drove 50 mph. how long, in hours, did it take lucy's friend to catch up to lucy?

Answer 1

Answer:

It took Lucy's Friend 2 hours to catch up to Lucy

Step-by-step explanation:

Since we are looking for the time in which both Lucy and her friend meet up, we can assume at a certain time they are both in the same location at a given time. Given this information we can equal both Lucy and her friend's distance from the house with the following equation.

$50*(x-.05) = 40x$

Where x is the amount of hours driven. We can now solve the equation to find at what time they meet up.

$50*(x-.05) = 40x$

$50x-25 = 40x$

$10x = 25$

$x = 2.5$

We can see that both Lucy and her friend meet up after 2.5 hours. But since Lucy's Friend left the beach 0.5 hours later, it took her 2 hours to catch up to Lucy.

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Answer 2

Lucy's friend makes up for Lucy's 20-mile head start at the rate of 10 miles per hour. Lucy's friend will catch up with Lucy after (20 mi)/(10 mi/h) = 2 hours.