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QuestionJaden runs 120 feet in 4.2 seconds. Jael runs 50 feet. Find their speeds in MPH.

Studdy Solution

STEP 1

Assumptions1. Jaden can run120 feet in4. seconds. Jael can run50 feet in the same time as Jaden3. We want to convert their speed to miles per hour (MPH)
4. There are5280 feet in a mile5. There are3600 seconds in an hour

STEP 2

First, we need to calculate the speed of Jaden in feet per second (fps). We can do this by dividing the distance he runs by the time it takes.
SpeedJaden=DistanceJadenTimeJadenSpeed_{Jaden} = \frac{Distance_{Jaden}}{Time_{Jaden}}

STEP 3

Now, plug in the given values for the distance and time for Jaden to calculate his speed.
SpeedJaden=120 feet.2 secondsSpeed_{Jaden} = \frac{120\, feet}{.2\, seconds}

STEP 4

Calculate the speed of Jaden in fps.
SpeedJaden=120 feet4.2 seconds=28.57 fpsSpeed_{Jaden} = \frac{120\, feet}{4.2\, seconds} =28.57\, fps

STEP 5

Now, we need to convert the speed of Jaden from fps to MPH. We can do this by multiplying the speed in fps by the conversion factor from feet to miles (1 mile is5280 feet) and the conversion factor from seconds to hours (1 hour is3600 seconds).
SpeedJaden=28.57 fps×1 mile5280 feet×3600 seconds1 hourSpeed_{Jaden} =28.57\, fps \times \frac{1\, mile}{5280\, feet} \times \frac{3600\, seconds}{1\, hour}

STEP 6

Calculate the speed of Jaden in MPH.
SpeedJaden=28.57 fps×1 mile5280 feet×3600 seconds1 hour=19.5 MPHSpeed_{Jaden} =28.57\, fps \times \frac{1\, mile}{5280\, feet} \times \frac{3600\, seconds}{1\, hour} =19.5\, MPH

STEP 7

Now, we need to calculate the speed of Jael in fps. We can do this by dividing the distance he runs by the time it takes. Since we are assuming that Jael runs50 feet in the same time as Jaden, we can use the same time for Jael.
SpeedJael=DistanceJaelTimeJaelSpeed_{Jael} = \frac{Distance_{Jael}}{Time_{Jael}}

STEP 8

Now, plug in the given values for the distance and time for Jael to calculate his speed.
SpeedJael=50 feet4.2 secondsSpeed_{Jael} = \frac{50\, feet}{4.2\, seconds}

STEP 9

Calculate the speed of Jael in fps.
SpeedJael=50 feet4.2 seconds=11.9 fpsSpeed_{Jael} = \frac{50\, feet}{4.2\, seconds} =11.9\, fps

STEP 10

Now, we need to convert the speed of Jael from fps to MPH. We can do this by multiplying the speed in fps by the conversion factor from feet to miles ( mile is5280 feet) and the conversion factor from seconds to hours ( hour is3600 seconds).
SpeedJael=.9 fps× mile5280 feet×3600 seconds hourSpeed_{Jael} =.9\, fps \times \frac{\, mile}{5280\, feet} \times \frac{3600\, seconds}{\, hour}

STEP 11

Calculate the speed of Jael in MPH.
SpeedJael=11.9 fps× mile5280 feet×3600 seconds hour=8. MPHSpeed_{Jael} =11.9\, fps \times \frac{\, mile}{5280\, feet} \times \frac{3600\, seconds}{\, hour} =8.\, MPHJaden is running at19.5 MPH and Jael is running at8. MPH.

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