SOLUTION: A master painter can paint a house in M days and two workers require W1 and W2 days each to paint a house alone. If the master can work as fast as the two workers working together
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Question 67413This question is from textbook Advanced mathematics
: A master painter can paint a house in M days and two workers require W1 and W2 days each to paint a house alone. If the master can work as fast as the two workers working together, write an expression for M in terms of W1 and W2. This question is from textbook Advanced mathematics
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Master Painter can paint 1/M houses per day
Worker1 can paint 1/W1 houses per day
Worker2 can paint 1/W2 houses per day
Now we are told that:
1/M=1/W1+1/W2 First get rid of fractions by multiplying both sides by the LCM which is MW1W2
W1W2(M/M)=MW2(W1/W1)+MW1(W2/W2) simplifying we get:
W1W2=MW2+MW1 and this equals:
W1W2=M(W1+W2) divide both sides by (W1+W2)
M=W1W2/(W1+W2)
