2. Suppose you are considering buying a Toyota Prius, which starts at $25,000 and gets 50 mpg. A similarly equipped Honda Accord will start at $22,000 but will get 31 mpg.
(a) How many miles will it take the Prius to recoup the price difference?

If a gallon of gas costs $2.9

The Prius can drive 50 miles with one gallon.

then for m miles, it needs:

(m/50) gallons.

and each gallon costs $2.9

Then for driving m miles, the cost would be:

(m/50)*$2.9

Then the total cost of buying the Prius and driving for m miles is:

P(m) = $25,000 + (m/50)*$2.9

We can do a similar approach for the Accord's case.

The Accord can drive 31 miles with one gallon.

Then if it drives m miles, it will need:

(m/31) gallons.

And knowing that each gallon costs $2.9, the cost for driving m miles is:

(m/31)*$2.9

Then the total cost of buying an Accord and driving for m miles is:

A(m) = $22,000 + (m/31)*$2.9

We want to find the value of m, such that the cost of the Prius is smaller than the cost of the Accord.

Then the first thing we need to find is the value of m such that the costs are equal:

P(m) = A(m)

$25,000 + (m/50)*$2.9 = $22,000 + (m/31)*$2.9

$25,000 - $22,000 = (m/31)*$2.9 -  (m/50)*$2.9

$3,000 = m*$2.9*(1/31 - 1/50)

$3,000/($2.9*(1/31 - 1/50)) = m = 84,392

This means that if you drive more than 84,392 miles, then the cost of the Prius will be smaller.

I

answer:

what is your question that you ask

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."