Direct proportion question

An ice manufacturing machine requires 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 ran for half an hour, find the mass of ice produced when thr machine ran for 7/4 hours.

Ok so i did m=kh (m is mass and h is hours )
20=k 1/2
K=40

When k=40, m= 70 tonnes.
However, the answer says 95 tonnes. Am i missing something here? Can someone help pls.

Posted from TSR Mobile

Yes you are failing to take account of the time the machine needs to warm up.

How do i include that into the equation?

Posted from TSR Mobile

How do i include that into the equation?

Posted from TSR Mobile

You don't need to if you don't want to. Just assume the machine runs for 20 mins instead of 30.

It is easy to include it the equation though. I'll let you think about it a bit more.

Ok assuming it runs for 20 mins then i've got k=60
Hence m=60 (7/4-1/6)
m=95.

Perfect! Thank you!

Posted from TSR Mobile

Well done.

If you want a formula that includes the 1/6 it would be:

$m = 60(h-\frac{1}{6})$ but I guess you have already realised that.