finding unit measure

Question

a car travels 180 miles in 4 hours. what is the car's speed in feet per second

Answer 1

Hi Sunnia, let's try to tackle this problem together:

 

 

• Problem tells us: Car travels 180 miles in 4 hours
• We want to know: How fast does the car go every second in feet

 

 

We can start by setting up a ratio and factoring down from there:

 

 

4 hours :: 180 miles

 

2 hours :: 90 miles

 

1 hour :: 45 miles

 

 

 

We've simplified the original information to learn that the car travels 45 miles every hour. Now, we can use this new information, along with the following information to find the answer.

 

 

• 60 seconds = 1 minute
• 60 minutes = 1 hour
• 1 mile = 5280 feet

 

 

(45 miles / 1 hour) * (1 hour / 60 minutes) * (1 minute / 60 seconds) * (5280 ft / 1 mile) = 66 ft / s

Answer 2

You will find the multiplicative identity (that is, 1) very useful in algebra because any number multiplied by it does not change value (although it may change units).  [Note: there is also an additive identity; know what it is?]

 

We are going to keep the same speed; just change the units:

    180 miles per 4 hours

    (180 miles)/(4 hours)

    ((180 miles)/(4 hours))*1

    ((180 miles)/(4 hours))*( (5280 ft)/(1 mile) )*((1 hour)(60 minutes))*((1 minute)/(60 seconds))

        Notice how miles, hours and minutes cancel out, leaving only feet and seconds

    ((180)/(4))*(5280)*(1/60)*(1/60)  ft/sec             [note: I write that way to paste into Excel]

     66 ft/sec

 

Another note:  PLZ don't jump to quickly to plain numbers; always get the correct units!

Answer 3

First we need to make sure that distance is in feet instead of miles.

 

convert the miles to feet

 

180 * 1609.344 * 3.3

 

= 955950.34ft

 

Secondly convert the hrs to seconds

 

T = 3600*4

 

= 14,400 feet

 

Finally use the formula for speed time 

 

Speed = 955,950.34/14,400

 

= 66.385ft/sec