Question

Darren drives to school in rush hour traffic and averages 36 mph. he returns home in mid-afternoon when there is less traffic and averages 48 mph. what is the distance between his home and school if the total traveling time is 1 hr 45 min?

Answer 1

The distance between Darren's home and school is 36 miles, calculated by setting up equations for each part of the trip and solving for the distance based on his speeds and the total traveling time of 1.75 hours.

Step-by-step explanation:

To find the distance between Darren's home and his school when he drives at different speeds during different times of the day, we need to use the formula: distance = speed × time.

First, let's convert the total traveling time of 1 hour and 45 minutes into hours since speed is given in miles per hour. 1 hour and 45 minutes is equivalent to 1.75 hours.

Let's let d represent the one-way distance from home to school. We can set up two equations based on the given speeds:

• In rush hour traffic, Darren drives to school at 36 mph, so the time it takes him to get to school is d/36.
• When returning home with less traffic at 48 mph, the time it takes is d/48.

The total time for both trips is the sum of the individual times: d/36 + d/48 = 1.75

To solve for d, we first need to find a common denominator for the fractions which is 144. Therefore, the equation becomes:

4d + 3d = 144 × 1.75

Then we get:

7d = 252

Now divide both sides by 7:

d = 252 / 7

d = 36 miles

So the distance between Darren's home and school is 36 miles.