Ms L was late getting to the harbor and missed the boat by 5 hours. The boat can go 528 miles in 24 hours. What should she do?

Question

take a speedboat that travels 100 miles in 2.5 hours or take a helicopter that goes 90 mph but takes 3.5 hours to get to the harbor

Answer 1

You want her to be able to catch up to the boat.

Whichever mode of transportation she takes, the 

distance she travels will have to equal the distance

the boat travels.

 

You will use the equation: Rate x Time = Distance

 

Boat travels 528 miles in 24 hours, therefor its rate is:

 

528 / 24 = 22 mph

 

Let X be the time for the boat, therefor the distance 

traveled by the boat will be:

 

Distance by boat  = 22X

 

Speedboat goes 100 miles in 2.5 hrs., its rate is

 

100 / 2.5 = 40 mph

 

Speedboat time is:  X - 5  (left 5 hrs later)

 

Distance of speedboat: 40 (X - 5)

 

Set distances of boat and speedboat equal to one another

 

       22X = 40 (X - 5)

 

       22X = 40X - 200

 

        200 = 18X

 

 11.1 hrs. = X (time of boat)

 

Speedboat will travel for 11.1 - 5 = 6.1 hrs

 

Distance is 40 (6.1) = 244 miles

 

Helicopter goes 90 mph

 

244 miles / 90 mph = 2.71 hrs + 3.5 hrs to get to the harbor = 6.21 hrs.

 

Speedboat will get to the boat quicker