Problema Solution
rita, britany. ab maria can complete a jigsaw in 1 hour and 30 minutes if they work together. Working alone, it takes rita 1 less hour to complete the jigsaw puzzle than it takes britany, and britany completes the jigsaw puzzle three times as fast as maria. How much time would it take each to complete the jugsaw puzzle working alone?
Answer provided by our tutors
let
r = the time rita needs to finish the jigsaw alone, r>0, thus her rate is 1/r jigsaws per hour
b = the time britany needs to finish the jigsaw alone,b>0, thus her rate is 1/b jigsaws per hour
m = the time maria needs to finish the jigsaw alone,m>0, thus her rate is 1/m jigsaws per hour
of they work together they complete the jigsaw in 1 hour and 30 min or 1.5 hours
1/r + 1/b + 1/m = 1/1.5
Working alone, it takes rita 1 less hour to complete the jigsaw puzzle than it takes britany
r = b - 1
and britany completes the jigsaw puzzle three times as fast as maria
b = 3m => m=b/3
plug r = b - 1 and m=b/3 into 1/r + 1/b + 1/m = 1/1.5
1/(b - 1) + 1/b + 1/(b/3) = 1/1.5
by solving we find
b = 7.72 hours
we do not take in consideration the second room 0.78 since in that case we get negative value for r
click here to see the step by step solution of the equation
b = 7.72 hours
r = b - 1 = 7.72 - 1 = 6.72 hours
m=b/3 = 7.72/3 = 2.57 hours
rita needs 6.72 hours to finish the jigsaw alone.
britany needs 7.72 hours to finish the jigsaw alone.
maria needs 2.57 hours to finish the jigsaw alone.