# Awoman drives an suv that gets 15 mi/gal (mpg). her husband drives a hybrid that gets 65 mpg. every

Awoman drives an suv that gets 15 mi/gal (mpg). her husband drives a hybrid that gets 65 mpg. every week, they travel the same number of miles. they want to improve their combined mpg. they have two options on how they can improve it.
option 1: they can tune the suv and increase its mileage by 2 mpg and keep the hybrid as it is.
option 2: they can buy a new hybrid that gets 80 mpg and keep the suv as it is.
which option will give them a better combined mpg?
compute the combined mpg for each option.
(round to one decimal place as needed.)

## This Post Has 7 Comments

1. roxannaemigdio3850 says:

Hey, there are no numbers added to this problem but if you were to add them as I did down below that is how you solve this question!

Step-by-step explanation:

Suppose s and h are the mileage numbers for the SUV and Hybrid, respectively. Then if each vehicle drives 1 mile, the total gas consumption is

.. 1/s +1/h

Then the combined mileage is

.. 2/(1/s +1/h) = 2sh/(s+h)

Option 1: s=12, h=60

.. mpg = 2*12*60/(12+60) = 20

Option 2: s=11, h=75

.. mpg = 2*11*75/(11 +75) = 1650/86 ≈ 19.2

In summary,

.. Option 1: 20.0 mpg

.. Option 2: 19.2 mpg

2. 1hannacarson says:

Let total gallon consumed  by SUV in a week when it is travelling at a speed of 13 mpg = x gallon

Total distance traveled by SUV in a week =13 x miles

and by hybrid , total gallons consumed when it is travelling at a speed of 60 mpg = y gallon

Total distance traveled by Hybrid in a week = 60 y miles

Case 1:

When mileage of SUV= 14 mpg

Total distance traveled by Hybrid  in a week = 14 x

Total distance traveled by SUV in a week = 60 y

14 x=60 y, as distance traveled by both cars in a week is same.

Average of two cars

$=\frac{14x+60y}{2}\\\\=\frac{14 x+14 x}{2}\\\\=14 x$

Case 2:

Mileage of new Hybrid = 85 mpg

Then total distance traveled by Hybrid in a week= 85 y

As, distance traveled by SUV in a week = 13 x

13 x=85 y, as distance traveled by both cars in a week is same.

So, Average of two cars

$=\frac{13x+85 y}{2}\\\\=\frac{13 x+13 x}{2}\\\\=13 x$

So, Option 1 will be better choice, they can tune the SUV and increase its mileage by 1 mpg and keep the hybrid as it is.

3. guko says:

The best option would be Number 1.

Step-by-step explanation:

Let's say that they each traveled 1,000 miles a week, meaning that instead of the SUV using 100 gallons of gas, it would be using 90.9, which is 9.1 gallons less.

The hybrid will only use 20 gallons of gas in that week. Meaning together, they will be 100.9 gallons a week for 1,000 miles.

In option 2, they would still be using 100 gallons of gas for the SUV a week, except, the hybrid would only be using 12.5 gallons, which is 7.5 gallons less.

The total of those together would be 112.5 gallons a week for 1,000 miles. So, it may be a small difference between the two options, yet Option 1 is the best choice on how to save gas.

4. ayoismeisalex says:

You can work this problem the same way the similar problem was worked at

Option 1: 2/(1/16 +1/65) = 25.7 mpg

Option 2: 2/(1/14 +1/85) = 24.0 mpg

As before, improving the least-efficient vehicle gives best resuls.

5. justicejesusfreak says:

Option 1 is the best one

Step-by-step explanation:

Let's call x the number of miles travelled by the woman. Then the combined miles travelled are 2*x  .

The number of gallons consumed is, for example, x/14 for the original SUV

.

The combined mpg is: combined miles travelled/combined gallons consumed. For the original case:

$\frac{2*x}{\frac{x}{14}+\frac{x}{65}}$

$\frac{2*x}{\frac{79}{910}*x}$

$\frac{2*910}{79}$

$23 \; mpg$

Option 1:

$\frac{2*x}{\frac{x}{16}+\frac{x}{65}}$

$\frac{2*x}{\frac{81}{1040}*x}$

$\frac{2*1040}{81}$

$25.7 \; mpg$

Option 2:

$\frac{2*x}{\frac{x}{14}+\frac{x}{85}}$

$\frac{2*x}{\frac{99}{1190}*x}$

$\frac{2*1190}{99}$

$24 \; mpg$

6. cmariecarrizales says:

Suppose s and h are the mileage numbers for the SUV and Hybrid, respectively. Then if each vehicle drives 1 mile, the total gas consumption is
.. 1/s +1/h
Then the combined mileage is
.. 2/(1/s +1/h) = 2sh/(s+h)

Option 1: s=12, h=60
.. mpg = 2*12*60/(12+60) = 20

Option 2: s=11, h=75
.. mpg = 2*11*75/(11 +75) = 1650/86 ≈ 19.2

In summary,
.. Option 1: 20.0 mpg
.. Option 2: 19.2 mpg

It usually works out best to increase the efficiency of the least-efficient contributor, as here.

7. lightning1157blaze says:

Option 1 would be best