Person A can paint the​ neighbor's house 3 times as fast as Person B. The year A and B worked​ together, it took them 10 days. How long would it take each to paint the ​ house?

Answer 1

Mags,

Translating this problem to math is tricky indeed. For example, Mason’s answer shows a trap we can get into: he mixed “days to paint a house” with its reciprocal: “fractions of a house per day”. Notice he says A is 3 times as fast as  B, but has a solution with A taking 3 times the number of days.

First explicitly name the quantities involved.

Let a be the fraction of a house A can paint in a day

Let b be the fraction of a house B can paint in a day.

In other words, a is A’s RATE, not A’s TIME

Now translate the problem into math.

First sentence:

a = 3 b 

Second sentence:

10a + 10b = 1

In other words, the fraction of a house A can paint in 10 days, plus the fraction B can paint in 10 days adds up to 1 house.

10(3b) + 10b = 1

40b = 1 house

b = 1/40 of a house

a = 3/40 of a house

Now, how many days does A take?  40/3 days

B takes 40 days.

If you have any questions, please ask

Answer 2

A=3(B) Person A is 3 times as fast as B.

A+B=10 A and B take 10 days.

A=? B=? How long does each take?

A=3B Given

3B+B=10 Substitute 3B for A

4B=10 Combine Like terms

B=10/4=5/2=2.5 days Solve for B

A=3(2.5)=7.5 days Solve for A

LOGIC CHECK: Earlier we said (the problem said) that person A is three times as fast as person B (A=3B). Is this true? YES! Person B takes 2.5 days, while person A takes 7.5. 3(2.5)=7.5