help please

Question

Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the best estimate of the speed Morris is traveling?

1 mile = 5,280 feet

Answer 1

When working with miles per hour and feet per second, it is very useful to find close equivalents.  For example, I calculated this for engineering class (and for driver's test) years ago, then I memorized it :   60 mph is 88 fps.

So, what is 1 mph?    (make sure the units cancel to leave   ft/sec)

            (1 mile / 1 hr ) *(5280 ft / 1 mile) * (1 hr / 60 min) * (60 sec / 1 min) =  1.466667 ft/sec

***   Wow! This means that 2 mph is approximately 3 ft/sec !   (comfortable walking speed)   ***

Morris is traveling approximately 48 miles per hour.

(p.s., also remember that PI is approximately 22/7 because problems often have a radius of 7 or 14 or 21.  I call these “magic numbers” because they allow you to cancel quickly and solve the problem.  Using 3.1415926 is also an estimate, but it usually requires a calculator or computer  -- I used a slide rule in engineering class).

Answer 2

First, we need to have consistent units.  We have miles and feet here.  Also, we have different units of time.  Lets use the given conversion factor for length and another conversion factor for time.

 

3600 sec = 1 hr

 

 

Let's use the unit miles per hour.

 

Since Aneesha has the units we want to use, we need to convert Morris'.

 

 

Set up a proportion to find Morris' distance in miles.

 

1 / x  = 5280 / 3

 

 

Cross multiply.

 

5280x = 3

       x = 0.000568 miles

 

so

 

3 feet = 0.000568 miles

 

Now we convert his seconds to hours.

 

1 sec = (1 / 3600) hr

1 sec = 0.000278 hr

 

 

Finally, we can divide the two numbers to get miles per hour.

 

(0.000568 miles) / (0.000278 hr) = 2.043 miles per hour

 

 

Here are the speeds of the two people.

 

Aneesha = 50 mph

Morris = 50 mph - 2.043 mph = 47.957 mph