Question

Wendy can wash a car twice as fast as Jason. When they work together, Wendy and Jason can wash a large van in 2 hours. How many hours would it take Jason to wash the van by himself? (1 point)
Question 20 options:

1) 5

2) 3

3) 4

4) 2

Answer 1

I won't give you a direct answer, but you know it can't be 2.

Answer 2

3 @heretohelpalways

Answer 3

?? @heretohelpaways

Answer 4

There's multiple ways to solve this. Here's an interesting approach as I wasn't too familiar with these sorts of word problems.

Since Wendy performs twice as fast as Jason, at any given moment whilst the car is being washed, Wendy will have completed twice as much of the car as Jason (as is obvious from the question).

Therefore, let w% be the percentage of the car that Wendy washed.

We know that the percentage of the car that Jason has washed at any given time is half that of Wendy, so let the percentage of the car that Jason has washed at any given moment be w%/2.

Therefore, w% + w%/2 = 100% for a completely washed car.

Solving this for w%, we can see that Wendy has washed just 66.66% of the car when the car is complete (by definition, Jason must have washed 33.33% of the car).

Therefore, if it takes Jason 2 hours to wash 33.33% of the car. How long would it take him to wash 100% of the car by himself? We can easily extrapolate and put this into an equation as 33.33% * x = 100% = 2 * x, where x is our multiplier.

Solving for x, x = 100%/33.33% = 3. Therefore, 2 * x = 2 * 3 = 6 hours.

A simpler approach would be to calculate (1/w + 1/(2w)) * x = 1. Where x represents the hours it takes to wash the car, w represents the fraction of the car washed each hour, and 1 is percentage of car washed by the addition of both Wendy and Jason washing for 2 hours (which is 100%, this is the reason we use 1).

We know already that they spend 2 hours washing the car for it to be completely washed, so we can replace x with 2, giving (1/w + 1/(2w)) *2 = 1.

Now what about those w's? We know already w is the fraction of the car that Wendy is washing. Since Jason is twice as slow as wendy, we make the coefficient of wendy 2 for Jason, since this is an inverse fraction, as we increase w (multiply it by 2), we are decreasing the efficiency of Jason. This makes sense.

After multiplying out we have 2/w + 1/w = 1. Solving for w we get, w = 3 hours (for Wendy).

Since we know Jason takes twice as long as Wendy, Jason takes 2*w = 6 hours to complete.

In both scenarios, Jason has taken 6 hours to wash the car. None of the options given however are correct, therefore we can conclude that none of the provided answers in the original question are correct.

Answer 5

i woulda figured that since it took 2 hours to do it together it would take 4 hours by himself cus i mean with two people you cut the time in half...