Work Rate Practice Worksheet
Expressions · Equations · Quadratics — 5 Variations
Packing Goodie Bags — Tomo & Benjamin
[5 marks]Tomo and Benjamin are helping the school to pack goodie bags for the students.
(a) Tomo takes y minutes to pack a goodie bag. Write down an expression in terms of y, for the number of goodie bags Tomo can pack in an hour.
Answer ______________________ [1]
(b) Benjamin takes 1 minute longer than Tomo to pack a goodie bag. Write down an expression in terms of y, for the number of goodie bags Benjamin can pack in an hour.
Answer ______________________ [1]
(c) Tomo and Benjamin together can pack a total of 64 goodie bags in an hour. Form an equation in y and show that it reduces to
[3]
(d) Solve the equation 16y2 − 14y − 15 = 0.
Answer y = _______ or _______ [2]
(e) How many goodie bags can Tomo pack in 3 hours?
Answer ______________________ [1]
Making Sandwiches — Alice & Ben
[5 marks]Alice and Ben are preparing sandwiches for a school event.
(a) Alice takes x minutes to make one sandwich. Write down an expression in terms of x, for the number of sandwiches Alice can make in an hour.
Answer ______________________ [1]
(b) Ben takes 2 minutes longer than Alice to make one sandwich. Write down an expression in terms of x, for the number of sandwiches Ben can make in an hour.
Answer ______________________ [1]
(c) Alice and Ben together can make a total of 32 sandwiches in an hour. Form an equation in x and show that it reduces to
[3]
(d) Solve the equation 4x2 − 7x − 15 = 0.
Answer x = _______ or _______ [2]
(e) How many sandwiches can Alice make in 1 hour?
Answer ______________________ [1]
Folding Boxes — Mei Ling & Wei Jie
[5 marks]Mei Ling and Wei Jie are folding cardboard boxes for a charity drive.
(a) Mei Ling takes t minutes to fold one box. Write down an expression in terms of t, for the number of boxes Mei Ling can fold in an hour.
Answer ______________________ [1]
(b) Wei Jie takes 1 minute longer than Mei Ling to fold one box. Write down an expression in terms of t, for the number of boxes Wei Jie can fold in an hour.
Answer ______________________ [1]
(c) Mei Ling and Wei Jie together can fold a total of 27 boxes in an hour. Form an equation in t and show that it reduces to
[3]
(d) Solve the equation 9t2 − 31t − 20 = 0.
Answer t = _______ or _______ [2]
(e) How many boxes can Mei Ling fold in 3 hours?
Answer ______________________ [1]
Wrapping Gifts — Sarah & Tom
[5 marks]Sarah and Tom are wrapping gifts for a school charity event.
(a) Sarah takes m minutes to wrap one gift. Write down an expression in terms of m, for the number of gifts Sarah can wrap in an hour.
Answer ______________________ [1]
(b) Tom takes 4 minutes longer than Sarah to wrap one gift. Write down an expression in terms of m, for the number of gifts Tom can wrap in an hour.
Answer ______________________ [1]
(c) Sarah and Tom together can wrap a total of 40 gifts in an hour. Form an equation in m and show that it reduces to
[3]
(d) Solve the equation m2 + m − 6 = 0.
Answer m = _______ or _______ [2]
(e) How many gifts can Sarah wrap in 3 hours?
Answer ______________________ [1]
Making Paper Cranes — Lily & Grace
[5 marks]Lily and Grace are making paper cranes for a school art exhibition.
(a) Lily takes k minutes to make one paper crane. Write down an expression in terms of k, for the number of paper cranes Lily can make in an hour.
Answer ______________________ [1]
(b) Grace takes 1 minute longer than Lily to make one paper crane. Write down an expression in terms of k, for the number of paper cranes Grace can make in an hour.
Answer ______________________ [1]
(c) Lily and Grace together can make a total of 22 paper cranes in an hour. Form an equation in k and show that it reduces to
[3]
(d) Solve the equation 11k2 − 49k − 30 = 0.
Answer k = _______ or _______ [2]
(e) How many paper cranes can Lily make in 1.5 hours?
Answer ______________________ [1]