QuestionA helicopter flies at $150 \mathrm{mi/h}$ from noon, overtaking a train that left at 9:00 am. Find the train's average speed.

Studdy Solution

STEP 1

Assumptions1. The helicopter travels at an average speed of150 mi/h. The helicopter left the terminal at noon3. The train left the terminal at900 am4. The helicopter overtook the train at00 pm5. Both the helicopter and the train travel at a constant speed

STEP 2

First, we need to calculate the time the helicopter and the train were in motion until the helicopter overtook the train.
The helicopter started at noon and overtook the train at200 pm, so it was in motion for2 hours.
The train started at900 am and was overtaken at200 pm, so it was in motion for5 hours.

STEP 3

Next, we need to calculate the distance both the helicopter and the train traveled until the helicopter overtook the train. Since they both traveled the same distance, we can use the speed of the helicopter and the time it was in motion to find this distance.
$Distance = Speed_{helicopter} \times Time_{helicopter}$

STEP 4

Now, plug in the given values for the speed of the helicopter and the time it was in motion to calculate the distance.
$Distance =150 \, mi/h \times2 \, h$

STEP 5

Calculate the distance.
$Distance =150 \, mi/h \times2 \, h =300 \, mi$

STEP 6

Now that we have the distance, we can find the average speed of the train. We can do this by dividing the distance by the time the train was in motion.
$Speed_{train} = Distance / Time_{train}$

STEP 7

Plug in the values for the distance and the time the train was in motion to calculate the average speed of the train.
$Speed_{train} =300 \, mi /5 \, h$

STEP 8

Calculate the average speed of the train.
$Speed_{train} =300 \, mi /5 \, h =60 \, mi/h$ The average speed of the train is60 mi/h.

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QuestionA helicopter flies at $150 \mathrm{mi/h}$ from noon, overtaking a train that left at 9:00 am. Find the train's average speed.

Studdy Solution

STEP 1

Assumptions1. The helicopter travels at an average speed of150 mi/h. The helicopter left the terminal at noon3. The train left the terminal at900 am4. The helicopter overtook the train at00 pm5. Both the helicopter and the train travel at a constant speed

STEP 2

STEP 3

STEP 4

Now, plug in the given values for the speed of the helicopter and the time it was in motion to calculate the distance.
$Distance =150 \, mi/h \times2 \, h$

STEP 5

Calculate the distance.
$Distance =150 \, mi/h \times2 \, h =300 \, mi$

STEP 6

Now that we have the distance, we can find the average speed of the train. We can do this by dividing the distance by the time the train was in motion.
$Speed_{train} = Distance / Time_{train}$

STEP 7

Plug in the values for the distance and the time the train was in motion to calculate the average speed of the train.
$Speed_{train} =300 \, mi /5 \, h$

STEP 8

Calculate the average speed of the train.
$Speed_{train} =300 \, mi /5 \, h =60 \, mi/h$ The average speed of the train is60 mi/h.

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QuestionA helicopter flies at 150mi/h150 \mathrm{mi/h}150mi/h from noon, overtaking a train that left at 9:00 am. Find the train's average speed.

Studdy Solution

STEP 1

Assumptions1. The helicopter travels at an average speed of150 mi/h. The helicopter left the terminal at noon3. The train left the terminal at900 am4. The helicopter overtook the train at00 pm5. Both the helicopter and the train travel at a constant speed

STEP 2

STEP 3

STEP 4

Now, plug in the given values for the speed of the helicopter and the time it was in motion to calculate the distance.Distance=150 mi/h×2 hDistance =150 \, mi/h \times2 \, hDistance=150mi/h×2h

STEP 5

Calculate the distance.Distance=150 mi/h×2 h=300 miDistance =150 \, mi/h \times2 \, h =300 \, miDistance=150mi/h×2h=300mi

STEP 6

Now that we have the distance, we can find the average speed of the train. We can do this by dividing the distance by the time the train was in motion.Speedtrain=Distance/TimetrainSpeed_{train} = Distance / Time_{train}Speedtrain​=Distance/Timetrain​

STEP 7

Plug in the values for the distance and the time the train was in motion to calculate the average speed of the train.Speedtrain=300 mi/5 hSpeed_{train} =300 \, mi /5 \, hSpeedtrain​=300mi/5h

STEP 8

Calculate the average speed of the train.Speedtrain=300 mi/5 h=60 mi/hSpeed_{train} =300 \, mi /5 \, h =60 \, mi/hSpeedtrain​=300mi/5h=60mi/hThe average speed of the train is60 mi/h.

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QuestionA helicopter flies at $150 \mathrm{mi/h}$ from noon, overtaking a train that left at 9:00 am. Find the train's average speed.

Now, plug in the given values for the speed of the helicopter and the time it was in motion to calculate the distance.
$Distance =150 \, mi/h \times2 \, h$

Calculate the distance.
$Distance =150 \, mi/h \times2 \, h =300 \, mi$

Now that we have the distance, we can find the average speed of the train. We can do this by dividing the distance by the time the train was in motion.
$Speed_{train} = Distance / Time_{train}$

Plug in the values for the distance and the time the train was in motion to calculate the average speed of the train.
$Speed_{train} =300 \, mi /5 \, h$

Calculate the average speed of the train.
$Speed_{train} =300 \, mi /5 \, h =60 \, mi/h$ The average speed of the train is60 mi/h.