a motorboat leaves the harbour and travels at an average spe

a motorboat leaves the harbour and travels at an average speed of 9mph toward a small island. Two hours later a cabin cruiser leaves the same harbour and travels at an average speed of 12 mph toward the same island. In how many hours after the cabin cruiser leaves the harbour will it be alongside the motorboat?

Solution

Let x= number of hours \'till the motorboat and cruiser will be alongside
Distance(d)=rate(r) times time(t) or d=rt
rate for motorboat=9 mph
rate for cruiser=12 mph
When they have both traveled the same distance, they will be alongside
Distance motorboat travels=18+9x (remember, motorboat had a 2 hour head start)
Distance cruiser travels=12x
So our equation to solve is:
18+9x=12x subtract 9x from both sides
18+9x-9x=12x-9x collect like terms
18=3x divide both sides by 3
x=6 hours -----------------number of hours \'till they are alongside
CK
18+9(6)=12(6)
18+54=72
72=72