Question

jayden and chandra are cleaning the house. it has 12 rooms, and each room is about the same size. when jayden cleans by himself, it takes him 6 hours. when chandra cleans by herself, it takes her 12 hours. when they clean the house together, they finish in 4 hours. when they work together, how many rooms does jayden clean and how many does chandra clean?

Answer 1

Jayden's work rate is twice Chandra's work rate, and, the rooms cleaned

by Jayden is twice the number of rooms cleaned by Chandra.

Response:

• Jayden cleans 8 rooms while Chandra cleans 4 rooms

Which method can be used to find the number of rooms cleaned by Jayden and Chandra?

Number of rooms in the house = 12

The time that Jayden takes to clean the house = 6 hours

Time that it takes Chandra to clean the house by herself = 12 hours

Time it takes both of them to clean the house = 4 hours

Required:

The number of rooms that Jayden clean and the number of rooms that

Chandra cleans when they work together.

Solution:

Given that the time it takes Jayden to clean the house is half the time

taken by Chandra.

Therefore;

The number of rooms Jayden cleans in 4 hours is twice the number of rooms cleaned by Chandra, which gives;

Ratio of the number of rooms cleaned by Jayden to the number cleaned by Chandra is 2 : 1

Total number of rooms cleaned = 12

$Number \ of \ rooms \ cleaned \ by \ Jayden = \dfrac{2}{2 + 1} \times 12 = \underline{8 \ rooms}$

The number of rooms cleaned by Chandra = 12 - 8 = 4 rooms

Learn more about ratios here:

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