Question

As Felicia gets on the freeway to drive to her cousin's house, she notices that she is a little low on
gas. There is a gas station at the exit she normally takes, and she wonders if she will have to get
gas before then. She normally sets her cruise control at the speed limit of 70mph and the freeway
portion of the drive takes about an hour and 15 minutes. Her car gets about 30 miles per gallon
on the freeway, and gas costs $3.50 per gallon.
a. Describe an estimate that Felicia might do in her head while driving to decide how many
gallons of gas she needs to make it to the gas station at the other end.

Answer 1

A. To estimate the amount of gas she needs, Felicia calculates the distance traveled at 70 mph for 1.25 hours. She might calculate
70⋅1.25=70+0.25⋅70=70+17.5=87.5 miles.

Since 1 gallon of gas will take her 30 miles, 3 gallons of gas will take her 90 miles, a little more than she needs. So she might figure that 3 gallons is enough.

Or, since she is driving, she might not feel like distracting herself by calculating 0.25⋅70 mentally, so she might replace 70 with 80, figuring that that will give her a larger distance than she needs. She calculates
80⋅1.25=80+14⋅80=100.

So at 30 miles per gallon, 313 gallons will get her further than she needs to go, so should be enough to get her to the gas station.

B. Since Felicia pays $3.50 for one gallon of gas, and one gallon of gas takes her 30 miles, it costs her $3.50 to travel 30 miles.

$3.5030 miles≈$0.121 mile, meaning it costs Felicia 12 cents to travel each mile on the freeway.

Answer 2

Estimation involves using a convenient value, close to the actual value, for calculations; especially in the absence of a calculator. The estimated number of gallons she needs to get to the station is 3 gallons.

Given that:

$Speed= 70mph$

$Time = 1.25hr$ ---- equivalent of 1hr 15mins

$Rate = 30 m/gallon$

First, she will need to estimate the distance she can cover using:

$Distance= Speed \times Time$

An estimate of the calculation is:

$Distance= 70mph \times 1.5 = 105m$

The number of gallons is then estimated as follows:

$Gallons = D ista nce\div Rate$

Because the estimated distance is 105 m; she can use 35 as an estimate the rate of miles per gallon; instead of 30

$Gallons = 105m \div 35m/gallon$

$Gallons = 3gallon$

So, the estimated number of gallons she needs is 3 gallons.

We can check if the estimate is true or close by calculating the actual values.

$Distance= Speed \times Time$

$D i s t a n c e= 70mph \times 1.25hr=87.5m$

$Gallons = D ista nce\div Rate$

$Gallons = 87.5m \div 30m/gallon =2.92m$

Hence, the estimated number of gallons she needs to get to the station is 3 gallons.

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