Inverse Proportion Word Problems

If 5 workers take 16 days to complete an order, how many days would it take 10 people?

Tags

CCSS.6.RP.A.3B

The time taken for a water heater to boil water is inversely proportional to the power of the water heater. When the power is 2000 Watts it takes 240 seconds to boil the water. Find the time it takes to boil water when the power is reduced to 1000 Watts.

• 120 seconds

• 360 seconds

• 600 seconds

• 480 seconds

Answer explanation

The time taken is inversely proportional to power, so when power is halved to 1000 Watts, the time will double to 480 seconds.

The time taken for passengers to be checked-in for a flight is inversely proportional to the number of staff working. It takes 30 minutes for passengers to be checked-in when 5 staff are working. How long will it take if 15 staff are working?

• 40 minutes

• 10 minutes

• 25 minutes

• 20 minutes

Answer explanation

The time taken for passengers to be checked-in is inversely proportional to the number of staff. If it takes 30 minutes with 5 staff, it will take 10 minutes with 15 staff (30/5=6, 6*15=90).

The number of days to complete research is inversely proportional to the number of researchers who are working. The research takes 125 days to complete if 5 people work on it. Find how many people are needed to complete the research in 25 days?

• 25

• 30

• 35

• 20

Answer explanation

To complete the research in 25 days, 25 researchers are needed. The number of researchers is inversely proportional to the number of days, so 5 researchers for 125 days means 25 researchers for 25 days.

The time required to build a house is inversely proportional to the number of builders, all working at the same rate. If there are 6 builders, it takes 80 days to complete the house. How many builders must be employed to build the house in just 16 days?

• 30

• 24

• 18

• 12

Answer explanation

To build the house in 16 days, the number of builders must be doubled. Therefore, 12 builders must be employed to complete the house in just 16 days.

The amount of sheep in a field is inversely proportional to the time taken for them to eat all of the grass in the field. When there are 100 sheep in a field it takes them 28 days to eat all the grass. How long will it take if there are 200 sheep in the field?

• 21 days

• 62 days

• 7 days

• 35 days

Answer explanation

When the number of sheep doubles to 200, the time taken for them to eat all the grass will be halved to 14 days due to the inverse proportionality relationship.

It takes 14 hours for a tap with a flow of 18 litres per minute to fill a reservoir with water. How long will it take if its flow is reduced to 7 litres per minute?

• 36 hours

• 10.5 hours

• 43 hours

• 26 hours

Answer explanation

To find the time taken with the reduced flow rate, use the formula: Time = Volume / Flow Rate. So, Time = Volume / 7. Since the volume remains the same, the time taken will be 14 hours.

Tags

CCSS.6.EE.B.7

4 people can paint a fence in 3 hours. How many people are needed to complete the job in half an hour?

• 24

• 12

• 6

• 10

Answer explanation

Two people are needed to complete the job in half an hour, as they can work together to finish it faster.

Tags

CCSS.6.RP.A.3B

A fort had provisions for 300 men for 90 days. After 20 days, 50 men left the fort. How long would the food last at the same rate?

• 108 days

• 120 days

• 95 days

• 84 days

Answer explanation

The food would last for 100 days. Since 50 men left, the remaining 250 men would consume the provisions at the same rate, doubling the duration.

Tags

CCSS.6.RP.A.3B

The force exerted by a magnet on a metal object is inversely proportional to the square of the distance. When the object is 2 cm away, the force exerted is 50 Newtons. How much force is exerted when the object is 10 cm away?

• 5 Newtons

• 100 Newtons

• 25 Newtons

• 2 Newtons

Answer explanation

The force exerted is inversely proportional to the square of the distance. Using the formula F = k/(d^2), where k is a constant, we can find the force when the object is 10 cm away by setting up the equation: 50 = k/(2^2) and solving for k. Then, plug in 10 for d to find the force.