pre calc question

Question

Logan leaves school to walk home. His friend, Maia, notices 0.5 hours later that Logan forgot his phone at the school. So Maia rides her bike to catch up to Logan and give him the phone. If Logan walks at 4.2 mph and Maia rides her bike at 11.7 mph, find how long (in hours) she will have to ride her bike until she catches up to him.

Round your answer to 3 places after the decimal point (if necessary) and do NOT type any units (such as "hours") in the answer box.

Time for Maia to catch up to Logan:  hours

Answer 1

distance = rate×time

Let t = time

They will meet when the distance traveled by both is the same.

11.7t = 4.2(t + .5)

11.7t = 4.2t + 2.1

7.5t = 2.1

t = 2.1/7.5 = 0.28

Answer 2

w = walking speed = 4.2 mph

b = biking speed = 11.7 mph, half an hour later

distance d = 4.2h miles for the walker

distance d = 11.7(h-.5) miles for the biker

set them equal

11.7h - 5.85 = 4.2h

11.7h- 4.2h = 5.85

7.5h = 5.85

h = 5.85/7.5 = .78 of an hour when they meet

which is .78-.5 = .28th of an hour after the biker leaves

in .78 hr, the walker goes 4.2(.78) = 3.276 miles

in .78 hr the biker goes 11.7(.78-.5) = 11.7(.28) = 3.276 miles