If a car traveling at 60 mph is chasing a car travelling at 50 mph and is 1⁄4 mile behind, how many minutes will it take the first car to catch the second? if a $6,000 contribution is divided among charities a, b, and c in a ratio of 8: 5: 2, respectively, how much more, in dollars, does charity a receive than charity c? a mixture containing 6% boric acid is to be mixed with 3 quarts of a mixture which is 12% boric acid in order to obtain a solution which is 10% boric acid. how much of the 6% solution must be used?

Answers

1 -

Speed of 1st car = 50mph, Speed of the chasing car = 60mph

Relative speed of both the cars = 60- 50 = 10mph ( ∵ Subtracted because both are heading in a same direction)

Distance between the cars = 1⁄4 mile

∴ Time required to chase down the car = = = = ×60 minutes = 1.5 minutes (ans)

2 -

Total amount = 6000

Ratio of A,B,C is 8:5:2

So $6000  have to divided among A,B,C in 8,5,2 parts respectively.

total = 15 parts

So 1 part will be = 6000/15 = $400

So A will get 8 parts = 8×400 = $3200

B will get 5 parts = 5×400 = $2000

C will get 2 parts = 2×400 = $800

∴ A will get more money as compared to C.

3 -

let assume, x quarts of the 6% boric acid solution is mixed with the 3 quarts 12% boric acid. Total amount of mixture =(x+3) quarts

So the acid equation ⇒ (0.06x) + (0.12×3) = 0.1(x+3)

⇒ 0.06x + 0.36 = 0.1x + 0.3

⇒ 0.04x = 0.06

⇒ x = 1.5 quarts

∴ 1.5 quarts of the 6% solution must be used.

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.