2013 AMC 8 Problem 11

Question

Ted’s grandfather used his treadmill on

3

days this week. He went

2

miles each day.

On Monday he jogged at a speed of

5

miles per hour. He walked at the rate of

3

miles per hour on Wednesday and at

4

miles per hour on Friday.

If Grandfather had always walked at

4

miles per hour, he would have spent less time on the treadmill. How many minutes less?

1

2

3

4

5

Time equals distance divided by rate.

Compare the actual total minutes with

6

miles at

4

mph.

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Grandfather spent

\frac{2}{5}

hours jogging on Monday. He spent

\frac{2}{3}

hours walking on Wednesday and

\frac{2}{4}=\frac{1}{2}

hours on Friday. Converting these times to minutes, we get

\dfrac{2}{5} \cdot 60 = 24

minutes for Monday,

\dfrac{2}{3} \cdot 60 = 40

minutes for Wednesday, and

\dfrac{1}{2} \cdot 60 = 30

minutes for Friday. Therefore, Grandfather totaled

94

minutes of exercise throughout the week.

If he walked at a pace of

4

miles per hour each day, he would have spent

\frac{2}{4}=\frac{1}{2}

hours each day walking. This equals

\frac{2}{4} \cdot 60 = 30

minutes every day. If he did this for

3

days, he would have totaled

3 \cdot 30 = 90

minutes of exercise.

Therefore, Grandfather would have spent

94-90=4

fewer minutes on the treadmill.

Thus, D is the correct answer.

Problem 11 in other years