Algebraic Help!!

Question

Under certain conditions, sound can travel 768 miles per hour. Under these conditions, Alan hears thunder 45 seconds after seeing lightning. His friend, Ryan hears thunder after seeing the lightning in 30 seconds. What is the longest and the shortest possible distance that Alan and his friend are apart.

-The distance

-Mile traveled per second

-

Answer 1

so lets start by converting miles/hr to miles/sec. since there are 60 min/hr and 60 sec/min. we can convert to miles/sec by taking 768÷60÷60=.2133 miles/sec.

this means that every second, sound travels .2133 miles. so we can take the amount of time in seconds times the distance traveled per a second(.2133 miles) to find the displacement of each person.

Alan is 9.59 miles away from the lightning by .2133x45 = 9.59

Ryan is 6.39 miles away from the lightning by .2133x30 = 6.39

since both ryan and alan can be on either the same side of the lightning or opposite sides of the lightning, we can find the minimum and maximum distance they are apart.

if they are on the same side, they are the minimum distance of 9.59-6.39 = 3.2 miles apart

if they are on opposites sides, they are the maximum distance of 9.59+6.39 = 15.98 miles apart

Answer

miles/sec = .2133

shortest distance = 3.2 miles

longest distance = 15.98 miles