On a car trip, Rhett and Jessica each drove for part of the trip, and the total distance they drove

Question

On a car trip, Rhett and Jessica each drove for part of the trip, and the total distance they drove was under $220$ miles. Rhett drove at an average speed of $35 miles per hour left parenthesis mph right parenthesis$ , and Jessica drove at an average speed of $40 mph$ . Which of the following inequalities represents this situation, where $r$ is the number of hours Rhett drove and $j$ is the number of hours Jessica drove?

A.

$35 r plus 40 j greater than 220$

B.

$35 r plus 40 j less than 220$

C.

$40 r plus 35 j greater than 220$

D.

$40 r plus 35 j less than 220$

Accepted Answer

Choice B is correct. It&rsquo;s given that Rhett drove at an average speed of 35 miles per hour and that he drove for r hours. Multiplying 35 miles per hour by r hours yields 35 r miles, or the distance that Rhett drove. It&rsquo;s also given that Jessica drove at an average speed of 40 miles per hour and that she drove for j hours. Multiplying 40 miles per hour by j hours yields 40 j miles, or the distance that Jessica drove. The total distance, in miles, that Rhett and Jessica drove can be represented by the expression 35 r + 40 j . It&rsquo;s given that the total distance they drove was under 220 miles. Therefore, the inequality 35 r + 40 j &#60; 220 represents this situation. Choice A is incorrect. This inequality represents a situation in which the total distance Rhett and Jessica drove was over, rather than under, 220 miles. Choice C is incorrect. This inequality represents a situation in which Rhett drove at an average speed of 40 , rather than 35 , miles per hour, Jessica drove at an average speed of 35 , rather than 40 , miles per hour, and the total distance they drove was over, rather than under, 220 miles. Choice D is incorrect. This inequality represents a situation in which Rhett drove at an average speed of 40 , rather than 35 , miles per hour, and Jessica drove at an average speed of 35 , rather than 40 , miles per hour.

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