Direct and inverse proportions

Question

A machine which manufactures ice needs to be run for 10 minutes to warm up before the production of ice begins. The mass, in tonnes, of ice produced is directly proportional to the number of hours of production. Given that 20 tonnes of ice are produced when the machine runs for half an hour, find the mass of ice manufactured when the machine runs for 1.75 hours

Answer 1

ignoring the warmup time, or if the 10 minutes is included in the 1/2 hour, then

I=kh

20=k(1/2)

k = 40

I=40(1.75) = 70 tons of ice in 1.75 hours

with 10 minutes warmup time = 1/6 hour, not counted in the 1/2 hour, then

to keep it proportional

I =kh

20 =k(1/2 +1/6) = 2k/3

k = 30

I =30h

I =30(1.75 + 1/6) = 30(7/4+1/6) = 30(23/12) = 115/2 = 57.5 tons of ice