Question

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?

Answer 1

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 =
`(Distance)/(Relative speed)` =
`(1/4)/(10)` =
`(1)/(40) hour` =
`(1)/(40)`×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.