Question

Tyler swims at a constant speed, 5 meters every 4 seconds. How long does it take him to swim 114 meters? A certain shade of light blue paint is made by mixing 1 1/2 quarts of blue paint with 5 quarts of white paint. How much white paint would you need to mix with 4 quarts of blue paint? A factory produces 3 bottles of sparkling water for every 8 bottles of plain water. How many bottles of sparkling water does the company produce when it produces 600 bottles of plain water? For each of the previous three situations, write an equation to represent the proportional relationship.

Answer 1

a). It is given that Tyler swims 5 m in every 4 seconds. So we need to find the time taken to swim for 114 meters.

Thus,

5 m = 4 second

1 m = 4/5 second

1 m = 0.8 second

∴ 114 m = 114 x 0.8

= 91.2 seconds.

The equation to represent the proportional relationship is :

`$t = (4)/(5) \ d $`

or
`$t = 1(1)/(5) \ d $`

b).
`$13 (1)/(3)$` quarts of white paint is required to to mix with the 4 quarts of the blue paint.

There are
`$3 (1)/(3)$` quarts of white paint per quart of the blue paint because 5 divided by
`$1 (1)/(2)$` is equal to
`$3 (1)/(3)$`

i.e.
`$4 * 3(1)/(3) = 13(1)/(3)$`

The relationship is :

`$w = (10)/(3)\ b $`

`$w = 3(1)/(3)\ b $`

c). A factory manufactures 3 sparkling water bottles for every 8 plain water bottles.

8 plain water bottles = 3 sparkling water bottle

1 plain water bottle =
`$(3)/(8)$` sparkling water bottle

= 0.375

∴ 600 plain water bottle = 0.375 x 600

= 225 sparkling water bottle

The proportional relationship is :

`$p = (8)/(3) \ s $`

`$p = 2(2)/(3) \ s $`