Question

A woman drives an SUV that get 13 miles per gallon (mpg). Her husband drives a hybrid that’s gets 60 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 1 mpg and keep the hybrid as it is. Option 2: they can buy a new hybrid that’s gets 85 mpg and keep the SUV as it is.

Answer 1

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.