ALGEBRA WORD PROBLEMS DISTANCE RATE TIME

Problem 1 :

Tri City Taxi Company charges $3 for the first mile and $0.20 for every tenth of a mile thereafter. If your trip is measured in tenths of a mile, how far can you ride in a Tri City Taxi for $12.

Solution :

Charge for the first mile = $3

For one tenth of the mile = 0.20

Let x be the number of one tenth of the mile

3 + 0.2 x = 12

0.2x = 12 - 3

0.2x = 9

x = 9/0.2

x = 45

number of one tenth of the mile = 45

So, actual miles = 45/10 ==> 4.5 miles

Total number of miles he has covered = 5.5 miles.

Problem 2 :

Adam can rent an apartment in the city and walk to work for $615 per month. He can rent an apartment in the suburbs for $500 per month and take the train to work for $5 per day. How many days will he have to work per month to make either choice equal financially?

Solution:

Let x be the number of days he has to work per month.

$615 = $500 + $5x

500 + 5x = 615

5x = 615 - 500

5x = 115

x = 23 days

Problem 3 :

A company needs a faster computer to enhance its e-business capabilities. The computer can be purchased for $1890 or rented for $900 plus $90 per month. What is the maximum number of months the computer could be kept so that it is cheaper to rent than to buy?

Solution:

Let x be the number of months.

The cost of buying = $1890

The cost of renting = $900 + $90x

1890 > 900 + 90x

1890 - 900 > 90x

990 > 90x

x < 11

The maximum number of months the computer could be kept so that it is cheaper to rent than to buy is 10 months.

Problem 4 :

Jennifer’s telephone service costs $30 per month plus $0.15 for each local call. Long distance calls are extra. Last month, her bill was $63.50, and it included $18.50 in long distance charges. How many local calls did she make?

Solution:

Let the amount of local calls be x.

The bill amount = $63.50

Long calls = $18.50

63.50 = 30 + 18.50 + 0.15x

63.50 = 48.50 + 0.15x

63.50 - 48.50 = 0.15x

15 = 0.15x

x = 15/0.15

x = 100 calls

Problem 5 :

Better taxi service charges $3.00 for the first mile plus $0.20 for each additional mile. Best taxi service charges $6.00 for the first two miles plus $0.10 for each additional mile. How many miles will a person travel in order to spend an equal amount of money using either service?

Solution:

Let the person travels be x miles.

The cost for better taxi service

3 + (x - 1) 0.2 = 0.2x + 2.8

The cost for best taxi service

6 + (x - 2) 0.1 = 0.1x + 5.8

0.2x + 2.8 = 0.1x + 5.8

0.1x = 5.8 - 2.8

0.1x = 3

x = 30 miles

Problem 6 : doubt

A video store offers two yearly pricing plans:

A. $10.00 charge plus $2.50 for each movie rented.

B. $4.00 charge (total) for the first 4 movies rented plus $3.00 per movie. How many movies will a person need to rent in order to spend an equal amount of money using either plan?

Solution:

A: 10 + 2.5x

B: 4 + 3x

10 + 2.5x = 4 + 3x

3x - 2.5x = 10 - 4

0.5x = 6

x = 12 movies

Problem 7 :

The marina parking lot charges $9.20 for the first hour and $1.20 for each additional hour. The main street parking lot charges $2.00 for the first hour and $1.80 for each additional hour. For how many hours will the two lots charge an equal amount of money?

Solution:

Let for x hours the two lots charge on equal amount of money.

The marina parking lot charges 9.20 dollars

For the first hour and 1.20 dollars for each additional hour.

Total charge for x hour = 9.20 + (x - 1) 1.20

The main street parking lot charges 2.00 dollars for the first hour and 1.80 dollars for each additional hour.

Total charge for x hour = 2.00 + (x - 1) 1.80

Now, charge of both lots are equal

9.20 + (x - 1)1.20 = 2.00 + (x - 1) 1.80

9.20 + 1.20x - 1.20 = 2.00 + 1.80x - 1.80

8 + 1.20x = 1.80x + 0.20

1.80x - 1.20x = 8 - 0.20

0.50x = 7.80

x = 7.80/0.50

x = 13 hours

Problem 8 :

Jamie needs to lease a car. At Big City Nissan, Jamie can lease an Altima for $3,000 down plus $420 per month. Big City will also give her the first two months of her lease free. At Rye Town Nissan, they offer her the same car for $3960 down plus $400 per month. Rye Town will give her the first four months free. After how many months would both deals cost the same?

Solution:

The total cost at Big city Nissan: 2 months free, then $420x months

The total cost at Rye Town Nissan: 4 months free, then $400x months

420x + 3000 = 400x + 3960

420x - 400x = 3960 - 3000

20x = 960

x = 48