mike rented a car. he drove 30 miles and the fee was $22.50. ben rented a car from the same establishment. he drove 50 miles and his fee was $31.50.

Question

a) write an equation the represents the cost, y, of renting a car for x miles.

b) if mike rented a car and spent $21, how many miles did he drive?

c) what is the flat rate of the cab ride?

d) how much does it cost to travel 7 miles in a cab?

Answer 1

For this problem, the cost for renting a car is based on a flat rate of $/mile

You need to know that the rate = cost/distance

(a) That expression can be rearranged by multiplying both sides by distance: rate • distance = cost

The cost (y) = the rate ($/mile) times the distance driven (x): y ($) = rate ($/mi) • x (mi) with the units in ( )

You are given information to calculate the rate for two drivers:

For Mike, x = 30 miles and the cost = $22.50, and rate = cost/distance

rate = $22.50 / 30 miles = $0.75/mile

For Ben, x = 50 miles and the cost is $31.50; rate = $31.50 / 50 miles = $0.63

Ben pays a lower rate than Mike.

(b) for Mike's travel:

rearrange the equation cost = rate • distance to solve for distance by dividing both sides by rate:

cost / rate = distance • rate / rate

rewriting, distance = cost / rate = $21.00/($0.75/mile) = 28 miles

(c) You may have missed part of this question. Parts (c) and (d) questions make no sense since there is no information given for a "cab".