A remote control car travels 3,969 feet in 1 min 10 seconds. What is the cars speed in miles per hour?

Question

How to solve

Answer 1

To change units without changing the value, we use the multiplicative identity (that is, 1).  Any value multiplied by 1 results in itself.  For this problem:

   1 = (5280 ft) / (1 mi) = (1 mi) / (5280 ft)        [choose appropriate one]

   1 = (60 min) / (1 hr) = (1 hr) /(60 min)

   1 = (60 sec) / (1 min) = (1 min) / (60 sec)

 

The problem gives:

  3969 feet in 1 min 10 sec

  (3969 ft) / (1 min 10 sec)

  (3969 ft) / (60 sec + 10 sec)

  ( (3969 ft) / (70 sec) ) * 1

  ( (3969 ft) / (70 sec) ) * ( (60 sec) / (1 min) ) * ( (60 min) / (1 hr) ) * ( (1 mi) / (5280 ft) )

  (3969/70)*(60/1)*(60/1)*(1/5280) mi/hr           

                     [note: ft, sec, min cancel out, leaving only mi/hr]

  38.7 mi/hr    [rounded]

Answer 2

Beth, these can be fun to play with. What we want is for units to cancel out.

 

1 minute and 10 seconds is 70 seconds.

 

3969 ft/70 seconds x 60 seconds/1 hour

 

Seconds in the denominator in the first factor cancel out seconds in the numerator of the second, and we are left with 3402 ft/hour.

 

Hope this helps!