John walked 10 miles on Saturday. He walked twice as fast on the second 5 miles of his walk than he walked on the first 5 miles of his walk. Which expression represents the time he spent walking? Let x = John's speed on the first half of his walk.

Question

A. fifteen over x
B. five over three x
C. fifteen over two x
D. ten over three x

Answer 1

Let's say John's speed on the first 5 miles was x. Then his speed on the second 5 miles was 2x, since he walked twice as fast.

To find the time he spent walking, we need to divide the distance by the speed.

For the first 5 miles: Time = Distance / Speed = 5 / x

For the second 5 miles: Time = Distance / Speed = 5 / 2x

So the total time John spent walking is:

Total Time = Time for First 5 Miles + Time for Second 5 Miles

Total Time = 5/x + 5/2x

We can simplify this by finding a common denominator:

Total Time = (10 + 5) / 2x

Total Time = 15 / 2x

So the answer is C. fifteen over two x.

Answer 2

Edie can paint a wall in 3 hours. Dan can paint the same wall in 6 hours. If they work together, how many hours will it take Edie and Dan to paint the wall?
A. 1 hour
B. 1.5 hours
C. 2 hours
D. 4.5 hours

Answer 3

Let's let x be the number of hours it takes Edie and Dan to paint the wall together.

In 1 hour, Edie can complete 1/3 of the wall (since she can paint the whole wall in 3 hours). Similarly, in 1 hour, Dan can complete 1/6 of the wall.

Working together, in 1 hour they can complete:

1/3 (the fraction of the wall Edie can do) + 1/6 (the fraction of the wall Dan can do)

= 1/2 of the wall.

So we can set up the equation:

1/2 = 1/x

To solve for x, we can cross-multiply:

2x = 1

x = 1/2

So it will take Edie and Dan 1/2 hour, or 30 minutes, to paint the wall together.

The answer is not one of the choices given, so either the answer choices are incorrect or there was a mistake in the problem.