Question

Eugene wants to ride his bike at least 40 miles today. The first hour was mostly downhill and he rode 13 miles. Write and solve an inequality to find how many miles per hour Eugene needs to ride to meet his goal.

Answer 1

Eugene has to ride at least 27 more miles today, after having initially rode 13 miles. If we assume he has 3 hours left to ride, he must ride more than 9 miles per hour to reach his goal of 40 miles.

Step-by-step explanation:

The subject of this problem is to find out how many miles Eugene needs to ride per hour to meet his goal of at least 40 miles for the day. Eugene initially rode 13 miles downhill. So, he still has to ride at least 40 - 13 = 27 miles.

Let's say the remaining time Eugene has to ride today is 'x' hours. So, the inequality that represents this situation is: x (the speed he needs to ride per hour) > 27 (the remaining miles he has to ride).

To solve this inequality, suppose Eugene rides for 3 more hours today. Then the inequality becomes: x > 27/3. Simplifying this we get x > 9. So, Eugene needs to ride more than 9 miles per hour for the remaining 3 hours to achieve his goal.

Learn more about Inequality Problem

Answer 2

Rate ≥ 9 miles per hour

Step-by-step explanation:

Eugene wants to ride his bike at least 40 miles today, this means that distance ≥ 40 miles. The first hour was mostly downhill, and he rode 13 miles. He has 3 more hours to ride. Write and solve an inequality to find how many miles per hour Eugene

needs to ride to meet his goal.

Solution:

Eugene needs to ride at least 40 miles today. During the first hour he rode 13 miles. The remaining distance is:

Remaining distance ≥ 40 - 13

Remaining distance ≥ 27 miles

Since he has 3 more hours to ride; to meet his goal, the rate he needs to ride is:

Rate ≥ 27 miles / 3 hours

Rate ≥ 9 miles per hour