Having done literally hundreds of these, I don't know why I can't come up with the answer:
A boat is making a round trip to an island. On the way there, it goes 15 mph, and on the way back it goes 12 mph. If it takes the boat six minutes longer on the way back, what is the distance to the island.
I just can't seem to come up with the equation for the thing.
Anonymous
Favorite Answer
First, convert everything to the same set of units. Since you're using mph for the speed, use hours and miles for time and distance. So, now the boat takes 0.1 hours longer on the way back. Let's define some variables: t := time on the way to the island, d := distance to the island. As you can see, the time for the way back should be t+0.1.
So, now, given that d=rt you should be able to get your equations.
d = 15(t) on the way out
d = 12(t+0.1) on the way back
combing these two by substitution:
d = 15(t)
d/15 = t
- then subst -
d = 12(t+0.1)
d = 12(d/15 + .1)
d/12 = d/15 + .1
d = 12d/15 + 1.2
d - 12d/15 = 1.2
3d/15 = 1.2
d/5 = 1.2
d = 6
Six miles!