Ratios: Problem 15: Chapter 3

[Khalid]

4 sewing machines can sew shirts in the ratio 1:2:3:5. The fastest can sew a shirt in 2 hours. However =, the fastest machine breaks. How long will t take the other three machines to sew 3 shirts?

Solution

The first machine can sew 1x shirts, the second can sew 2x shirts, the third can sew 3x shirts and the fastest can sew 5x shirst. If the fastest machine can sew a shirt in 2 hours, its rate is 1/2 shirts/hour. We can use the rate of the fastest machine to solve for the unknown multiplier x.

5x = 1/2

What I am strugling with the above. How can we equate the rate to shirts produced? Thank!

[Joey Z.]

The three remaining sewing machines together have an efficiency rate of 1+2+3 = 6 compared to 5 of the fastest one. To sew 3 shirts, it takes the fastest sewing machine 2*3 = 6 hours, which means it'll take all three other machines 6*(5/6) = 5 hours.

[JonathanSchneider]

Perhaps the language of the problem was confusing you a bit. When it says "machines can sew shirts in a ratio of..." this really means that the rates are in a ratio of...

Do other people find this meaning ambiguous at all? The 11th edition doesn't phrase anything quite like this, so if this is a source of confusion we might want to update that.