Tish and Emma are knitting scarves. Tish's scarf is 17.7 inches long, and she knits 2 3/8 inches per minute. Emma's scarf is 4 inches long, and she knits 3 3/4 inches per minute. After how many minutes will Emma's scarf be longer that Tish's scarf?
To find the difference in length between Tish's scarf and Emma's scarf, we need to subtract the length of Tish's scarf from the length of Emma's scarf:
Emma's scarf length - Tish's scarf length
= 4 inches - 17.7 inches
= -13.7 inches
Now, we need to find the rate at which Emma is gaining length on Tish. Emma knits 3 3/4 inches per minute, while Tish knits 2 3/8 inches per minute. The difference in their knitting rates is:
3 3/4 inches/minute - 2 3/8 inches/minute
= 15/4 - 19/8
= 30/8 - 19/8
= 11/8 inches/minute
To find out how many minutes it will take for Emma's scarf to be longer than Tish's scarf, we need to divide the difference in length by the difference in their knitting rates:
-13.7 inches / (11/8 inches/minute)
= -13.7 inches * (8/11 minutes/inch)
= -9.818181818 minutes
Since we can't have a negative time, we take the absolute value of the result:
9.82 minutes
Therefore, it will take approximately 9.82 minutes for Emma's scarf to be longer than Tish's scarf.