Question

If anybody will check this for me, I know my answer is incorrect I just don't know where I messed up

Answer 1

Rate Problem: Jeff and Lucy have been asked to wash their mom’s minivan. It takes Jeff 2 hours to wash the van by himself, and it takes Lucy 1.5 hours to wash the van by herself. How long will it take Jeff and Lucy to wash the van if they work together?
a. What equation is used to solve this problem? What does each variable represent?

Use the equation w = rt, where w represents the number of vans to be washed, r represents the washing rate, and t represents the time spent washing.

b. Identify the given information.

Jeff’s time is 2 hours. So his rate is r = 1 van / 2hours
Lucy’s time is 1.5 hours. So her rate is r = 1 van / 1.5 hours
Jeff and Lucy are washing one van, so w = 1
The total time if Jeff and Lucy work together is unknown, so t represents the unknown variable.

c. Enter the given information into the equation.

1 = (1/2 + 1/1.5) t

d. Solve the equation.

Distribute t: 1 = t/2 + t/1.5
The LCM of 2 and 1.5 is 3.5, so the LCD is 3.
Multiply the LCD on both sides of the equation.

3 * 1 = 3 ( t/2 + t/1.5)
3 = 3t/2 + 3t/1.5
Cancel common factors
3 = t + 1.5t
Simplify
3 = 1.5t
3/1.5 = t
2 = t

Answer 2

***3 = 3t/2 + 3t/1.5
Cancel common factors
3 = t + 1.5t
****
You made a mistake with your arithmetic

notice that
3t/2 is 1.5t and 3t/1.5 is 2 t
so you have
3= 1.5t + 2t
3 = 3.5 t
or
\[ \frac{7}{2}t = 3\\ t= 3 \cdot \frac{2}{7}= \frac{6}{7}\]

Answer 3

I'm confused, I made a mistake with cancelling common factors?

Answer 4

I would start with
\[ (\frac{1}{2} + \frac{1}{1.5}) t = 1 \]
and write 1.5 as 3/2 and
\[ \frac{1}{\frac{3}{2}}= \frac{2}{3} \]
and the problem is
\[ (\frac{1}{2} +\frac{2}{3}) t= 1\]
we get
\[ (\frac{3}{6} + \frac{4}{6}) t= 1 \\ \frac{7}{6} t =1 \\ t= \frac{6}{7}\]

Answer 5

** I'm confused, I made a mistake with cancelling common factors? **

3 = 3t/2 + 3t/1.5 <--- this is ok
Cancel common factors
3 = t + 1.5t <--- this is wrong. what did you do ?

Answer 6

I'm not sure.

Answer 7

I don't know what I did wrong

Answer 8

Let's pick up with multiplying by 3 ( and leave the t outside the parens, it is simpler if we don't distribute it):
\[ (\frac{1}{2} + \frac{1}{1.5}) t = 1\]
multiply by 3:
\[ (\frac{1\cdot 3}{2} + \frac{1\cdot 3}{1.5}) t = 3 \]
now simplify. what do you get?

Answer 9

you should get
\[ ( \frac{3}{2} + \frac{3}{1.5}) t = 3 \\ (1.5+2.0) t = 3 \]

Answer 10

It is confusing (for me) to mix decimals and fractions. I would change 1.5 to 3/2
and 1/(3/2) to 2/3
(see post up above)

Answer 11

Okay then what do you do after (1.5 + 2.0)t = 3?

Answer 12

simplify 1.5 + 2.0

Answer 13

3.5

Answer 14

so now you have
3.5 t = 3

what next ? I would divide by 3.5

Answer 15

So you have t = 3/3.5

Answer 16

which is very ugly looking. you could do a few things.
one way to get rid of the decimal is multiply 3.5 by 10 to make it 35
but you have to multiply top and bottom by the same number so do
\[ t = \frac{3\cdot 10}{3.5 \cdot 10} \]

Answer 17

what do you get ?

Answer 18

30/35

Answer 19

yes. can you simplify that ? (divide top and bottom by 5)

Answer 20

6/7

Answer 21

which is the answer.


notice you could have used that trick at the start with
\[ \frac{1}{1.5} = \frac{10}{1.5\cdot 10} = \frac{10}{15}= \frac{2}{3} \]
to get rid of the decimal. Then the problem is easier (I think)

Answer 22

Thank you!