Question

1. Y varies inversely with x. If y = 9 when x = -5, find the value of x when y=-6.

2. Luke and Nora can peel 12 carrots in 5 min, working together. Luke can peel 5
carrots in 11 min, working alone. How many minutes would it take Nora to peel 8
carrots, working alone?

Answer 1

Explanation:

1 ) Y∝ 1 / X

Y = k / X

Y = 9 , X = -5

Putting the values in the relation above

9 = k / - 5

k = -45

Y = - 45 / X

Put Y = - 6

- 6 = - 45 / X

X = - 45 / -6

= 7.5

2 )

Luke and Nora can peel 12 carrots in 5 minutes

in 1 minute Luke and Nora can peel 12 / 5 carrot

in 1 minute Luke alone can peel 12/ 11 carrot .

In 1 minute Nora alone will peel (12 / 5 - 12/ 11 ) carrot

(12 / 5 - 12 / 11 )

= 2.4 - 1.1

= 1.3 carrot

In 1 minute Nora alone will peel 1.3 carrot

1.3 carrot in 1 minute

8 carrot in 8 / 1.3 minute

= 6.15 minutes.

In 1 minute Nora alone will peel 8 carrot in 6.15 minutes working alone.