SOLUTION: Jack and Danny are bricklayers. Jack can build a certain brick wall in 8 hours whereas Danny takes 11 hours. If they work together, their combined rate decreases by 7 bricks an hou

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Jack and Danny are bricklayers. Jack can build a certain brick wall in 8 hours whereas Danny takes 11 hours. If they work together, their combined rate decreases by 7 bricks an hou      Log On


   

Question 941032: Jack and Danny are bricklayers. Jack can build a certain brick wall in 8 hours whereas Danny takes 11 hours. If they work together, their combined rate decreases by 7 bricks an hour, and it only takes them 5 hours to build the wall together. Find the number of bricks in the wall.
The rate is constant throughout the time period. As an explicit example, if Jack can lay 10 bricks an hour, and Danny can lay 15 bricks an hour, then their combined rate is 10 + 15 - 7 = 18 bricks an hour.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +b+ = the number of bricks in the wall
Jack's rate:
+b%2F8+
Danny's rate:
+b%2F11+
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+b%2F8+%2B+b%2F11+=+%28+b%2B7+%29%2F5++
+%285%2F8%29%2Ab+%2B+%285%2F11%29%2Ab+=+b+%2B+7+
Multiply both sides by +88+
+55b+%2B+40b+=+88b+%2B+616+
+95b+-+88b+=+616+
+7b+=+616+
+b+=+88+
--------------
There are +88+ bricks in the wall
check:
+b%2F8+%2B+b%2F11+=+%28+b%2B7+%29%2F5++
+88%2F8+%2B+88%2F11+=+%28+88%2B7+%29%2F5++
+11+%2B+8+=+95%2F5+
+19+=+19+
OK
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I was confused about whether to add or subtract
the +7+ in +b%2F8+%2B+b%2F11+=+%28+b%2B7+%29%2F5++
The only way the equation can work is if I add
the +7+. I can force myself to make sense of it
if I say that +b%2B7+ has to be the "normal" rate
for them working together, and the +7+ makes
up for their loss of rate. Hope I got this- definitely
get another opinion.