Rick and Mike are roommates and leave Gainesville on Interstate 75 at the same time to visit their girlfriends for a long weekend. Rick travels north and Mike travels south. If Mike's average speed is 8 miles per hour faster than Rick's, find the speed of each if they are 210 miles apart in 1 hour and 30 minutes.

Answer: Rick and Mike are going in opposite directions. Then the distance between them as a function of time will be R = Vm * (time traveled) + Vr * (time traveled).

where Vm is the velocity of mike, Vr is the velocity of rick

then, if after 1 hour and 30 mins the distance between them is 210 miles.

we have 250 miles = Vm*1.5 h + Vr*1.5 h

i used 1.5 hours, because 1 hour and 30 minutes are 1.5 hours.

We also know that Vm = Vr + 8 miles.

so: 250 miles = Vr*1.5h + (Vr + 8miles/hour) * 1.5 = (2*vr + 8miles) * 1.5h

250/1.5 miles/hour - 8 miles/hour = 2*Vr = 158.66 miles per hour.

then Vr = 158.66 / 2 = 79.33 miles per hour.

and Vm = (79.33 + 8) = 87.33 miles per hour.