Use the space below to solve the following questions. Show all work.

1. Each floor in a hotel has the same number of rooms. A member of the housekeeping staff cleaning every room on 5 floors cleaned 50 rooms.

a. Write the unit rate in the form of rooms per floor. ( 2 points)

The unit rate of rooms per floor is:

r = number of rooms / number of floors

r = 50 / 5

r= 10 rooms / floor.

The unit rate of rooms per floor is 10 rooms per floor.

b. Use this unit rate to find how many rooms are in the hotel if there are 30 floors in all. Show your work. ( 2 points)

Since the unit rate of rooms per floor is 10 rooms per floor, if there are 30 floors in all, we have the following:

Rooms in the hotel = 10 rooms per floor x 30 floors

Rooms in the hotel = 300 rooms.

There are 300 rooms in the hotel.

2. A train traveled 92 miles in 2.5 hours before making an emergency stop. After the stop, it traveled 68 miles in 1.5 hours. Find the train’s average speed. Show your work. Round your answer to the nearest tenth. ( 2 points)

In order to find the train’s average speed, we need to find first the train’s speed before the emergency stop:

92 / 2.5 = 36.8 miles per hour

Then find the train’s speed after the emergency stop:

68 / 1.5 = 45.3 miles per hour

Finally, to find the average, we add the two average speeds and divide by the count (here two):

(36.8 + 45.3) / 2 = 82.1 / 2 = 41 miles per hour.

The train’s average speed is 41 miles per hour.

3. A store can develop 175 photos every half hour.

a. How many photos can be developed in 3 hours? (2 points)

Since we know that the store develops 175 photos per 0.5 hour, we need to find the rate of how many photos are developed per hour, then multiply by 3:

Photos developed per hour : 175 x 2 = 350 photos per hour

For 3 hours: 350 x 3 = 1,050 photos per hour. So the store develops 1,050 photos in 3 hours.

b. How many photos can be developed in 10 hours? ( 2 points)

Since we know that 350 photos are developed in 1 hour, we need to calculate the following to find how many photos can be developed in 10 hours:

350 x 10 = 3,500 photos in 10 hours.

So the store develops 3,500 photos in 10 hours.

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