Question

In the exercise, translate the statement to an equation or inequality and solve.

Leon drove from his house in Cincinnati to his sister’s house in Cleveland, a distance of 252 miles. It took him $4.5$hours. For the first half hour, he had heavy traffic, and the rest of the time his speed was five miles per hour less than twice his speed in heavy traffic. What was his speed in heavy traffic?

Short answer

The speed in heavy traffic is $27.3mph$

Step-by-step solution

Step 1. Given Information

We are given that Leon is driving a distance 252 miles in $4.5hr$. He drove half an hour in heavy traffic. In rest of the time his speed is 5 mph less than twice his speed in heavy traffic.

Step 2. Translation 

Let $xmph$is the speed in heavy traffic.

We will create the table to organize the given data.

	$Rate\times Time=Dis\tan ce$
Heavy traffic	$xmph$	role="math" localid="1644506537916" $0.5$	role="math" localid="1644506589030" $0.5x$
Rest of time	$2x+5$	4hr	$4(2x+5)$
252 miles

Since, total distance given is 252 miles. Thus, the required equation isrole="math" localid="1644506621610" $0.5x+4(2x+5)=252$

Step 3. Calculation

Solve the equation to find the value.

$$\begin{gathered} 0.5x+8x+20=252 \\ 8.5x=232 \\ x=27.3 \end{gathered}$$

Thus, the speed in heavy traffic is$27.3mph$