RATIOS RATES AND PROPORTIONS SAT PRACTICE

Problem 1 :

If an object travels at 15 feet per minute, how many feet does it travel in 1.5 seconds ?

Solution :

Distance traveled by the object = 15 feet

Time taken to travel the distance = 1 minute

Writing it as ratio, we get

15 : 1

1 minute = 60 seconds

Let x be the distance traveled by the object in 1.5 seconds.

60 : 15 = 1.5 : x

Using proportion,

Product of means = product of extremes

60x = 15(1.5)

x = 15(1.5)/60

x = 22.5/60

x = 0.375 feet

So,0.375 feet can be covered when 1.5 seconds is given.

Problem 2 :

How many pounds of flour are needed to make 15 rolls of bread if 20 pounds of flour are needed to make 100 rolls of bread?

Solution :

Let x be the number of pounds of flour needed.

20 pounds of flour are needed to make 100 rolls.

20 : 100 = x : 15

20(15) = 100 x

x = 20(15) / 100

x = 3

So, 3 pounds of flour is needed to make 15 rolls.

Problem 3 :

The ratio of 1.5 to 1 is equal to which of the following ratios ?

a)  1 to 2   b)  2 to 1    c)  3 to 1     d)  3 to 2

Solution :

The given ratio is, 1.5 : 1

In order to remove the decimal, we multiply both parts by 10.

= 15 : 10

= 15/10

= 3/2

= 3 : 2

So, the result is option d.

Problem 4 :

Worker A can install a toy in 12 minutes. Worker B takes 10 minutes to install the same toy. In 5 hours, how many more toys can be installed by worker B than worker A ?

a)  10   b)   8    c)  7    d)  5

Solution :

Number of minutes taken by worker A = 12 minutes

Number of minutes taken by worker B = 10 minutes

Time given for each = 5 hours

(or)

= 5 x 60

= 300 minutes

Let x be the number of toys can be installed by worker A in 300 minutes.

Let y be the number of toys can be installed by worker B in 300 minutes.

Difference = 30 - 25

= 5 toys.

Then worker B can install 5 more toys.

Problem 5 :

How many gallons are needed to travel 550 miles for a certain car that needs 17.5 gallons to travel 350 miles ?

Solution :

For 17.5 gallons of gas, the car can travel 350 miles.

17.5 : 350

Let x be the number of gallons of gas needed.

17.5 : 350 = x : 550

17.5/350 = x/550

x = (17.5/350) ⋅ 550

x = 27.5

So, 27.5 gallons of gas is needed to travel 550 miles.

Problem 6 :

How many more minutes would it take to burn a full of 640 gallon tank of gasoline for a certain rocket engine that can burn a full 480 gallon tank in 15 minutes?

Solution :

In 15 minutes it will burn 480 gallon.

In how many minutes 640 gallon tank will burn. Let x be the number of minutes taken.

15 : 480 = x : 640

15/480 = x/640

x = (15/480) ⋅ 640

x = 20

So, 20 minutes is the required number of minutes.

Problem 7 :

If 60 pounds of force can stretch a spring 5 inches, how many inches will the spring be stretched by a force of 84 pounds ? Assume the force needed to stretch a spring varies directly with its stretch distance.

Solution :

The length of spring = 5 inches

The length it can stretch = 60 pounds.

Let x be the required length of stretch with the force of 84 pounds.

5 : 60 = x : 84

5/60 = x/84

x = (5/60) ⋅ 84

x = 7

So, the required length of stretch is 7 feet. 

Problem 8 :

If John has $90 and he spends $30 on video games and $25 on food, what fraction of the original $90 does John have left ?

Solution :

Original amount he has = $90

Amount spent for food = $25

Amount spent for video games = $30

Amount left over = 90 - (25 + 30)

= 90 - 55

= 35

Fraction part of the amount left over = 35/90

= 7/18

So, 7/18^th of the money is left over.

Problem 9 :

John takes 8 minutes to bike 3 miles. At this rate, how many minutes will it take to bike 4.5 miles ?

Solution :

Distance to be covered in 8 minutes = 3 miles

Let x be the number of minutes taken to cover the distance of 4.5 miles.

8 : 3 = x : 4.5

8/3 = x/4.5

x = (8/3) (4.5)

x = 12 minutes.

So, to cover 4.5 miles distance, it will take 12 minutes.

Problem 10 :

If x/y = 4/5, what is the value of 10x/4y ?

Solution :

x/y = 4/5

x = 4y/5

10x/4y = 10(4y/5) / 4y

= 2(4y) / 4y

= 2/1

So, the value of 10x/4y is 2.