WORD PROBLEMS ON RATE AND UNIT RATE

Problem 1 :

Five lemons cost $1.80.

a) what is the cost per lemon?

b) At this rate, what is the cost of 9 lemons?  

Solution :

Cost of 5 lemons = $1.80

a) To find the cost per lemon, we will divide the total cost by by the number of lemon.

= 1.80/5

= $0.36

So, the cost per lemon is $0.36.

b) Cost of 9 lemons :

= 9 × 0.36

So, the cost of 9 lemons is 3.24.   

Problem 2 :

David hikes 2 1/4 miles in 1/2 an hour.

a) what is his rate in miles per hour?

b) At this rate, how long will it take him to walk 18 miles?

c) if he walks for 7 hours, how far will he have gone?

Solution :

David is taking 1/2 an hour to cover 2 1/4 miles.

a)  Distance covered in 1 hour

1/2 hour = 2  1/4 miles

Multiplying by 2 on both sides, we get

1 hour = (9/4) x 2

= 9/2

= 4  1/2

So, 4  1/2 miles per hour.

b) Distance to be covered = 18 miles.

Speed = 4 /12 miles per hour

Time = Distance / Speed

= 18 / 4  1/2

= 18/(9/2)

= 18 × 2/9

= 4 hours

So, David will cover 18 miles in 4 hours.

c) Time taken = 7 hours

Speed = 4 1/2 miles per hour

Distance = Time x speed

= 7 × 4  1/2

= 7 × 9/2

= 63/2

= 31  1/2

So, he has covered 31  1/2  miles.

Problem 3 :

Erica babysits for 4 1/2 hours and is paid $27.

a) How much does she make per hour ?

b) How much does she make for 8 hours ?

c) if the people she babysits for have $34 to pay her, how long can they stay out?

Solution :

Given, Erica babysits for 4 1/2 hours and is paid $27.

a) Charge for one hour = 27 / 4  1/2

= 27 / (9/2)

= 27 x (2/9)

= $6

So, Erica will get $6 per hour.

b) To find she make for 8 hours.

= 8 × 6

= 48

So, $48 she make for 8 hours.

c) Her charge is $6 for 1 hour. To find the hours taken to pay $34.

1 : 6 = x : 34

Product means = product of extremes

1 × 34 = 6 × x

34 = 6x

34/6 = x

5.7 = x

So, they can stay out 5.7 hours.

Problem 4 :

Michael is headed to his aunt’s house. For the first 2 hours he drives at 55 mph. For next hour, he drives 70 mph. For the final 2 hours he drives 50 mph.

a) How far does he travel?

b) what is his average speed for the entire trip?

c) If he drives the entire trip at 70 mph, how much less time will it take?  

Solution :

Speed for the first 2 hours = 55 mph

Speed for the next one hour = 70 mph

Speed of last two hours = 50 mph

a) Distance covered in first two hours = 55 × 2

= 110 miles

Distance covered in first two hours = 70 × 1

= 70 miles

Distance covered in first two hours = 50 × 2

= 100 miles

Total distance = 110 + 70 + 100

= 280 miles

So, Michael travels 280 miles.

b) To find average speed of the entire trip:

Average speed = Total distance covered / Total time taken

= 280 / 5

= 56

So, average speed of the entire trip is 56 mph.

c) Time taken to cover the total distance

 = 280/70

= 4

Time difference = 5 – 4

= 1

So, it will take 1 less hour to cover the distance.

Problem 5 :

John took a 5 1/2 mile walk to his friend’s house. He left at 11 am and arrived at his friend’s house at 1 pm.

a) what was his average speed of walking?

b) if the return trip took a half hour longer, how much lower was his average speed on the return trip than on the trip to his friend’s house?

Solution :

a) Time taken to reach his friend's house = 2 hours

Average speed = Total distance covered / Total time taken

= 5  1/2/2

= 11/2/2

= 11/4

= 2  3/4

So, average speed of walking is 2  3/4 miles per hour. 

b) Now the time taken is 2 1/2 hours.

Speed = 5  1/2 / 2 1/2

= (11/2) / (5/2)

= (11/2) x (2/5)

= 11/5

Difference speed = 2 3/4 - 11/5

= 11/4 - 11/5

= (55 - 44) / 20

= 11/20

= 0.5 miles

Problem 6 :

Tom jogged from 10:30 am. to 12:15 pm. He traveled a distance of 7 miles.

a) what was his average rate of jogging?

b) At 12:15 pm., he decided to go an additional 5 miles at the same rate. At what time should he finish the additional 5 miles.

Solution :

a) Tom jogged from 10:30 am. to 12:15 pm.

He traveled a distance of 7 miles.

10:30 a.m. to 12:15 p.m. = 1 hour 45 minutes

= 1  3/4 hour

7 miles is being covered in 1  3/4 hours.

Speed = 7 / 1  3/4

= 7 / (7/4) 

= 4 miles

So, average rate of jogging is 4 miles.

b) To cover additional 5 miles he will take 4 mph as speed.

Time = 5/4

= 1.25 hours.

= 1 hour 15 minutes.

To cover 5 miles, it will take 1 hour 15 minutes.