Solve this multi-step problem. A runner completes 1/4 of a 5-mile race every 8 minutes. At the same pace, how far can the runner go in 16 minutes?(1 point)

Question

Responses

1/8 mile

160 miles

2 1/2 miles

1/10 mile

Answer 1

To determine how far the runner can go in 16 minutes, we first need to calculate the pace of the runner per minute.

The runner completes \( \frac{1}{4} \) of a 5-mile race in 8 minutes.

First, we calculate how far that is in miles: \[ \frac{1}{4} \times 5 = 1.25 \text{ miles} \]

Next, we calculate the pace in miles per minute: \[ \text{Pace} = \frac{1.25 \text{ miles}}{8 \text{ minutes}} = 0.15625 \text{ miles per minute} \]

Now, to find out how far the runner can go in 16 minutes, we multiply the pace by the time: \[ \text{Distance in 16 minutes} = 0.15625 \text{ miles per minute} \times 16 \text{ minutes} = 2.5 \text{ miles} \]

Therefore, at the same pace, the runner can go \( 2.5 \) miles in 16 minutes.

The correct response is: 2 1/2 miles

Answer 2

A water tank decreases by 10 gallons every 3 hours every day. What is the total change in the amount of water in the tank after 6 days?(1 point)
Responses

−480 gallons
negative 480 gallons

−80 gallons
negative 80 gallons

480 gallons
480 gallons

80 gallons

Answer 3

To find the total change in the amount of water in the tank after 6 days, we can start by calculating the amount of water that decreases each day.

Given that the tank decreases by 10 gallons every 3 hours, we first need to determine how many 3-hour periods are in a day.

There are 24 hours in a day, so: \[ \text{Number of 3-hour periods in a day} = \frac{24 \text{ hours}}{3 \text{ hours per period}} = 8 \text{ periods} \]

Since the tank decreases by 10 gallons in each 3-hour period, the total decrease in one day is: \[ \text{Decrease in one day} = 10 \text{ gallons/period} \times 8 \text{ periods} = 80 \text{ gallons} \]

Now, to find the total decrease over 6 days: \[ \text{Total decrease in 6 days} = 80 \text{ gallons/day} \times 6 \text{ days} = 480 \text{ gallons} \]

Because the water is decreasing, we represent this change as negative: \[ \text{Total change} = -480 \text{ gallons} \]

Thus, the correct response is: −480 gallons or negative 480 gallons.