Some help with these maths problems?

Question

I need not only the answers to these questions, but also, how they are to be figured out. Thanks!

1. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?


2 hours and 24 minutes, 3 hours and 12 minutes, 3 hours and 44 minutes, 4 hours and 10 minutes or 4 hours and 33 minutes.

2.A student receives his grade report from a local community college, but the GPA is smudged. He took the following classes: a 2 hour credit art, a 3 hour credit history, a 4 hour credit science course, a 3 hour credit mathematics course, and a 1 hour science lab. He received a “B” in the art class, an “A” in the history class, a “C” in the science class, a “B” in the mathematics class, and an “A” in the science lab. What was his GPA if the letter grades are based on a 4 point scale? (A=4, B=3, C=2, D=1, F=0)

2.7, 2.8, 3.0, 3.1 or 3.2.

Thanks again!

Answer 1

1.
S = house /4hr
J = house/6 hr
S + J = house /4hr + house/6 hr
(S + J) = house(1 /4hr + 1/6 hr)
house/(S + J) =1/(1 /4hr + 1/6 hr)
house/(S + J) =12 hr/(12 hr/4hr + 12 hr/6 hr)
house/(S + J) =12 hr/(3 + 2)
house/(S + J) =12 hr/5
house/(S + J) =2 hr 24 min.

2.
2*3 = 6
3*4 = 12
4*2 = 8
3*3 = 9
1*4 = 4
---------
13 GPA = 39
GPA = 3.00

Answer 2

1. Let x = the time together
x/4 + x/6 = 1 (whole house painted)
x=12/5 hours = 2 h 24 min

2. Total hours = 2 (art) + 3 (history) + 4(science) +3(math) 1 (science) = 2+3+4+3+1 = 13
Total points = 2(3) + 3(4) + 4(2) + 3(3) + 1(4)
= 6+12+8+9+4 = 39
GPA = 39/13 = 3

Answer 3

1 They are working in parallel. The formula (used in electronics when resistors are in parallel) is (A*B)/(A+B)

(6*4)/(6+4) = 24/10 = 2 and 4/10
1/10 of an hour is 6 minutes, so 4/10 = 24 minutes
Total: 2 Hours 24 minutes.

Hope that gets you started...

Answer 4

1.Sally can paint 1 house in 4 hours.So in 1 hour she can paint 1/4 of a house.In 1 hour John can paint 1/6 of a house.
1/4+1/6=6/24+4/24=10/24
=5/12
So they can paint 5/12 of a house in an hour.So to paint 1/12 of a house they will take 12 minutes.
12minX12=144min
=2hr 24 min
As for question 2......I dunno what is a GPA so i cant solve that question.Sorry

Answer 5

hproblem # 1 it took me about 3o m to fugue it out .here

when sally paint 3 house in 12 hours John will pain 2 ouses in the same 12 hours so 3/2 =1.5 so sally works more than john in one and half time . any way.
so if john was y sally works like 3/2 y, so y+3/2y are gonna paint a house y +3/2y=2/2y+3/2y=5/2y you follow me.

so we john paint the house in 6 hours so y take 6 hours360m but both together 5/2y take c hours
360 divide by 5/2 so 720/5=144m so it is 2 hours and 24m

Answer 6

I looked at the first 2 ansers and am ver convused as far as I see it
1) if John would tak 6 hours and sally 4 together they can do it in 5 halfe the tiome of each as they work together in reality it would probably be less but add the times and 1/2 it

sorry these multypul choice convuse me

Answer 7

1. Sally's paint rate is 0.250 houses per hour, and John's is 0.166 houses per hour, so together they can do 0.416 houses per hour. So, it would take 2.4 hours.

2. Multiply the hours by the grade value for each course, and add up the products. Separately, add up the hours for each course, and divide the first sum by the second.