Question

PLEASE HELP!!!

Word Problem:
Roy is attending his cousin's graduation ceremony in another town. Roy has already driven 30 miles and the ceremony starts in 2 hours.

a.) Let r represent Roy's driving speed in miles per hour. Write an expression to show the total distance Roy will have driven in 2 hours.

b.) The graduation is 150 miles from Roy's home. Use this information and your expression from Part (a) to write an inequality showing the possible speeds Roy could drive to make it to the ceremony on time.

c.) Solve your inequality and graph the solutions. What does your solution mean in the context of the problem?
I will add extra points to this question because there are 3 parts to it.

Answer 1

The standard formula is: distance = speed x time. From this, we know that speed = distance/time and that time = distance/speed.

a. If r = speed, then r = distance/time. From the information presented in "a", you cannot calculate Roy's speed.

b, c. Because the time is the limiting value in the question, use the "time" version of the formula: time = distance / speed

Because Roy must be at the ceremony in "less than or equal to" 2 hours, we set up an inequality.
2 <= distance / speed (which = r)
therefore, 2 <= distance / r

Because Roy has already travelled 30 miles, he has only 120 miles remaining.
2 <= 120 / r

Solve for "speed":
2r <= 120
r <= 60
You must be careful about how you interpret this answer. Remember hat "r" is the MINIMUM speed which solves the equation. Therefore, to make it to the wedding on time, Roy must drive at least 60 mph.
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