Neil drives at an average speed of 60 miles/hour to reach his destination 480 miles away. On the way back, he decides to increase his speed to try to save at least one hour. If the increase in his speed is x miles/hour, create an inequality to find the minimum increase in his speed.

480 / (60 + x) ≤ 7

Step-by-step explanation:

The average speed of Neil is:

d = v*t ⇒ t = d/v ⇒ t = 480 / 60 h ⇒ 8 h

That means Neil took 8 h in her trip

If we call x the increase in her speed back home

She needs at least go according to:

480 / (60 + x) ≤ 7

And this is the inequality to find the minimun increase in the speed, to show that we can solve the inequation, at the limit (that means when she saves just 1 hour)

480 / (60 + x) = 7

480 = 7 (60 + x)

480 = 420 + 7 x

7x = 60

x = 60/7 ⇒ x = 8.57 miles/hour (minimun increase)

Then the minimun speed would be

60 + 8,57 = 68.57 miles / h

Checking

480 / 68.57 = 7.0001 h