A master painter takes 4 hours to paint a wall and expects to be paid $45 per hour for his work. His apprentice takes 6 hours to paint the same sized wall and expects to be paid $20 per hour. How much will it cost to hire both the master painter and his apprentice to paint the wall together? 4 marks
theres more than 1 way to approach this question but the one id go with is
step 1, find both their respective speeds of painting per hour as a percentage of the wall per hour
for the master painter
in 1 hour he paints 1/4 of the wall, ie 25% per hour, at $45 per hour
for the apprentice
in 1 hour he paints 1/6 of the wall, ie 16.67% per hour, at $20 per hour
step 2 find their combined rate of work/cost
so in 1 hour of them both painting the wall, 25% + 16.67% = 41.67% of the wall painted per hour for $45 + $20 = $65 per hour
thus that is their combined rate of work
step 3 find the time they will take to finish the wall as a pair
to paint 100% of the wall it will take 100%/41.67% per hour = 2.4 hours