Question

Jack travels to work on the Eastern Freeway. He notices that the difference in time between if he drives 5 mph below the speed limit and if he drives 15 mph below the speed limit is 2 minutes. Given that the distance for which he uses the freeway is 10 miles, find the speed limit of the freeway.
55 mph
65 mph
60 mph
45 mph

Answer 1

Answer:

65 MPH

Step-by-step explanation:

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Answer 2

Let's denote s as the speed limit. To find the total time it takes for Jack to drive given the speed, we just divide the total number of miles he covered (10 miles) by the speed he's traveling at.

Accounting for the given of the problem, we'll have the following equation:
$\frac{10}{s-15} - \frac{10}{s-5}= \frac{1}{30}$ (from the fact that the difference between the time it takes to drive five miles below the speed limit versus 15 miles below is 2 mins or $\frac{1}{30}$ hours.)

Since we only have one unknown variable, we can freely solve for s:
$\frac{10}{s-15} - \frac{10}{s-5}= \frac{1}{30}$ 
$\frac{10(s-5)-10(s-15)}{(s-15)(s-5)}= \frac{1}{30}$ 
$\frac{10s-50-10s+150}{s^{2}-5s-15s+75}= \frac{1}{30}$ 
$\frac{100}{s^{2}-20s+75}= \frac{1}{30}$  
$3000=s^{2}-20s+75$
$0=s^{2}-20s-2925$
$s_{1}=65$
$s_{2}=-45$ (we ignore the negative value since there is no negative speed.)

ANSWER: The speed limit of the freeway is 65 mph.