Question

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. 7 + x 480 ≥ ≤ = x + 60 7 x + 480

Answer 1

Answer:

  480/(x+60) ≤ 7

Step-by-step explanation:

We can use the relations ...

  time = distance/speed

  distance = speed×time

  speed = distance/time

to write the required inequality any of several ways.

Since the problem is posed in terms of time (7 hours) and an increase in speed (x), we can write the time inequality as ...

  480/(60+x) ≤ 7

Multiplying this by the denominator gives us a distance inequality:

  7(60+x) ≥ 480 . . . . . . at his desired speed, Neil will go no less than 480 miles in 7 hours

Or, we can write an inequality for the increase in speed directly:

  480/7 -60 ≤ x . . . . . . x is at least the difference between the speed of 480 miles in 7 hours and the speed of 60 miles per hour

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Any of the above inequalities will give the desired value of x.