Question

a family drives to a forest cabin for a weekend getaway at 20 mph. the cabin is 105 miles from their city home. they are within 5 miles of the cabin when the absolute value of the difference between their distance from home and 105 miles is less that 5 miles. at what time range will the family be within 5 miles of the cabin?

Answer 1

To find the time range during which the family will be within 5 miles of the cabin, you can set up a simple equation. First, let's determine the distance remaining when they are within 5 miles of the cabin.

Distance from home to the cabin = 105 miles
When they are within 5 miles of the cabin, the remaining distance = 105 - 5 = 100 miles.

Now, we can calculate the time it takes to cover this remaining distance at a speed of 20 mph:

Time = Distance / Speed
Time = 100 miles / 20 mph
Time = 5 hours

So, it will take the family 5 hours to cover the remaining 5 miles to reach the cabin once they are within 5 miles of it.

Now, if we assume they start the journey at time t=0, they will be within 5 miles of the cabin between t=0 and t=5 hours. So, the time range during which the family will be within 5 miles of the cabin is from 0 to 5 hours.