Jack can paint a house in 5 days, and Richard can paint the same house in 7 days. Working together, how long will it take them to finish the job?

In order to simplify the problem, I will solve it without using fractions.

First,  we should find the least common multiple(LCM) of the days needed for Jack and Richard to paint a house. Normally, we would use a specific method to find the LCM but in this problem, we know that 7 and 5 are coprime( here a question might appear) numbers and, therefore, we can find it by multiplying the numbers => 7*5=35.

Now, we can say that Jack can paint 35 days/ 5 days = 7 houses. For the same time, Richard could paint 35 days/ 7days = 5 houses. Thus, if they worked together, they would paint 5+7=12 houses for 35 days.

We are asked to find how many days do Jack and Richard need to paint only one house. The answer would be 35 days/ 12 houses = 2 and 11/12 days

Answered by Kristiyan T. Maths tutor

3051 Views

See similar Maths 11 Plus tutors

Related Maths 11 Plus answers

All answers ▸

What is the sum of the factors of 21?


Jodie works for a bookshop. She is paid £6.50 an hour plus 5% of the cost of each book she sells. On Saturday, Jodie worked for 3 hours and sold £220 worth of books. How much money did Jodie earn?


How would I solve y=3x, 2x+y=5 using the substitiution method?


Barney has 12 items of fruit. Four of these are apples. If Lucy takes one of Barney's items of fruit at random what is the probability it will be an apple? What is the probability it will not be an apple?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2024

Terms & Conditions|Privacy Policy
Cookie Preferences