You are in a boat 2 miles from the nearest point on the coast. You are to go to point Q located 3 miles down the coast and 4 miles inland (see figure). You can row at a rate of 4 miles per hour and you can walk at a rate of 4 miles per hour. Toward what point on the coast should you row in order to reach point Q in the least time?
A)3 miles
B)8 miles
C)4 miles
D)1 mile
E)5 miles

Question

You are in a boat 2 miles from the nearest point on the coast. You are to go to point Q located 3 miles down the coast and 4 miles inland (see figure). You can row at a rate of 4 miles per hour and you can walk at a rate of 4 miles per hour. Toward what point on the coast should you row in order to reach point Q in the least time? 
A)3 miles 
B)8 miles 
C)4 miles 
D)1 mile 
E)5 miles

Quizplus · Accepted Answer

The shortest time to reach point Q is achieved by minimizing the time spent walking. This means we want to minimize the distance walked. Using the Pythagorean theorem, we can find that the direct distance from the starting point to point Q is 5 miles. If we row directly towards point Q, we will reach a point 3 miles down the coast and 0 miles inland (since we rowed directly towards Q, we don't need to walk inland at all). From there, we only need to walk 4 miles to reach point Q, for a total distance travelled of sqrt(3^2 + 4^2) + 4 = 5 + 4 = 9 miles. If we row towards a point closer to point Q but not directly at it, we will reduce the walking distance but increase the rowing distance. Therefore, we should row directly towards point Q, which means rowing 1 mile towards the coast.

You Are in a Boat 2 Miles from the Nearest