SOLUTION:
It takes George 1 hour longer to mow the lawn than it takes Henry. Working together, using two mowers, they can mow the lawn in 1 hour and 12 minutes. How long would it take He
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It takes George 1 hour longer to mow the lawn than it takes Henry. Working together, using two mowers, they can mow the lawn in 1 hour and 12 minutes. How long would it take He
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Question 255993:
It takes George 1 hour longer to mow the lawn than it takes Henry. Working together, using two mowers, they can mow the lawn in 1 hour and 12 minutes. How long would it take Henry to mow the lawn by himself?
[hint: Let x be the time taken by George. How much of the lawn does George mow in 1 hour? How much does Henry do in 1 hour? How much do they mow together in 1 hour?]
You can put this solution on YOUR website! Let the time taken to mow the lawn by Henry be x
Then,the time taken to mow the lawn by Henry be x+1
Using two movers they mow the lawn in 1h 12m = 1 12/60 h =1 1/5 = 6/5 h
So we have,
1/x +1/(x+1) = 1/(6/5)
(x+1+x)/x(x+1) = 5/6
6(2x+1) = 5x(x+1)
12x+6 = 5x^2+5x
0 = 5x^2-7x-6
5x^2-7x-6=0
(5x+3)(x-2)=0
x = -5/3 or 2
x cannot be negative.
So we get x = 2
Therefore the time taken to mow the lawn by Henry is 2 hours
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