Craig is the captain of a large cargo ship that is docked in New York City. He is staying at a hotel on the corner of 3 rd Street and 7 nd Avenue....

Question

Craig is the captain of a large cargo ship that is docked in New York City. He is staying at a hotel on the corner

of 3rd Street and 7th Avenue, while the boat is docked on the corner of 9th and 1st

as shown below. The distance between each street and each avenue is one block and each block is 0.25 miles.

4) Approximately many miles is Craig’s hotel from the boat dock? Please round your answer to the nearest

hundredth of a mile..

5) If Craig calls for a taxi to take him from the hotel to the dock, what is the least number of miles the taxi

driver can take him? Assuming the cab needs to stay on the roads!

Answer 1

The map of a city is very similar to the coordinate x-y axis. We can plot the two locations and find the vertical and horizontal distances. Then, use the Pythagorean theorem (the sum of the squares of the two legs is equal to the square of the hypotenuse) to find the distance.

Starting location: third street and 7th avenue (x = 3 and y = 7; coordinates (3,7)

Ending location: ninth and first (x = 9 and y = 1); coordinates (9,1)

horizontal distance: second x - first x: 9 - 3 = 6 (but each block is .25, so divide by 4) = 1.5 miles

vertical distance: second y - first y: 1 - 7 = -6 (but distance is always positive, so it is an absolute value)

Divided by 4 = 1.5 miles

Using Pythagorean theorem: 1.5^2 + 1.5^2 = distance squared

2.25 + 2.25 = distance squared

4.5 = distance squared

Now square both sides

Square root of 4.5 = distance

2.12 miles = distance between hotel and boat