word problem

Question

If a person were walking at the average speed of 2.5 mph from District 12 to District 13 and it takes a week to get there, how fast is the hovercraft traveling from District 12 to District 13, which makes it there in 45 min?

Answer 1

 Distance between district 12 & 13 = 2.5 miles/hr  *( 24 *7 hr) =  420 miles

 

  420 miles = (45 miles/hr) * h

 

   h = 420miles / ( 45min * 1hr/ 60minute) =

          

           420/ (3/4) = 560 miles / hr     Speed of hovercraft  

 

 

    Note : Distance formula is used

 

            D_{distance traveled in miles} = S_{speed miles/hr} * t _{traveling time} in hr

Answer 2

Hi Amy -- start with 168 hrs per week ... an hour is 1/3 bigger than 45 min ... rescale ...

 

boost 168 by 56 ... 224 hovercraft trips per week ... times 2.5 => double and add 1/2 ...

 

448 plus 112 ==> 560 mph ... Best regards, ma'am :)

Answer 3

Hi Amy;

person's speed is 2.5 miles/hour

45 minutes must be converted to 0.75 hours

I assume one week is seven days.  Considering the fact that the unit of 2.5 is in hours, we must convert the time of 7 days into hours.

(7 days)[(24 hours)/(1 days)

The unit of days is in the numerator and denominator.

These cancel...

(7 days)[(24 hours)/(1 days)

(7)(24 hours)

The only unit remaining is hours, which is what we want.

Let's calculate...

168 hours

distance=(rate)(time)
distance=(2.5 miles/hour)(168 hours)

The unit of hours is in the denominator and numerator.  It cancels...

distance=(2.5 miles/hour)(168 hours)

distance=(2.5 miles)(168)
distance=420 miles

 

distance=(rate)(time)

420 miles=(rate)(0.75 hours)

(420 miles)/(0.75 hours)=rate

The units are miles/hour.   This is what we want...

560 miles/hour