Math

QuestionA boat takes 2122 \frac{1}{2} hours and a plane takes 12\frac{1}{2} hour. How much faster is the plane than the boat?

Studdy Solution

STEP 1

Assumptions1. The time taken by the boat is 1 \frac{1}{} hours. The time taken by the airplane is 1\frac{1}{} hour3. The distance to the island is the same for both the boat and the airplane

STEP 2

First, we need to find the speed of each vehicle. Speed is calculated by dividing the distance by the time. Since the distance is the same for both the boat and the airplane, we can say that the speed is inversely proportional to the time.
Speed=1TimeSpeed = \frac{1}{Time}

STEP 3

Now, plug in the given values for the time taken by the boat and the airplane to calculate their speeds.
Speedboat=1212Speed_{boat} = \frac{1}{2 \frac{1}{2}}Speedplane=112Speed_{plane} = \frac{1}{\frac{1}{2}}

STEP 4

Convert the mixed number 2122 \frac{1}{2} to an improper fraction.
212=22 \frac{1}{2} = \frac{}{2}Speedboat=12Speed_{boat} = \frac{1}{\frac{}{2}}

STEP 5

Calculate the speed of the boat.
Speedboat=152=25Speed_{boat} = \frac{1}{\frac{5}{2}} = \frac{2}{5}

STEP 6

Calculate the speed of the airplane.
Speedplane=112=2Speed_{plane} = \frac{1}{\frac{1}{2}} =2

STEP 7

Now that we have the speeds of both the boat and the airplane, we can find how many times as fast as the boat the plane is. This can be done by dividing the speed of the plane by the speed of the boat.
Speedratio=SpeedplaneSpeedboatSpeed\, ratio = \frac{Speed_{plane}}{Speed_{boat}}

STEP 8

Plug in the values for the speeds of the plane and the boat to calculate the speed ratio.
Speedratio=225Speed\, ratio = \frac{2}{\frac{2}{5}}

STEP 9

Calculate the speed ratio.
Speedratio=225=5Speed\, ratio = \frac{2}{\frac{2}{5}} =5The plane is5 times as fast as the boat.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord