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What's wrong with my calculations here? Simple ratios and fractions..

Yeah so, I've studied towards level 4 maths in the past, but am apparently rusty..

Question:

"A company uses a time-rate method with bonus to pay its direct labour in one of its factories. The time-rate used is £10 per hour and workers are expected to produce 5 units an hour. Any time saved is paid at £9 per hour.
Bob worked for 35 hours last week and produced 185 units.

Calculate the gross wage earned by Bob for the week"
(forget gross, just the bonus calc)

I know there is an easy way to work out the answer, but I don't understand why my method failed and it's really bothering me, thanks.

So I divided 185 by 35 to give 5.2857143 units an hour. Then divided 300 by this number to see the number of minutes it took for 5 units to be produced on average which is 56.7567568 minutes, meaning we save 3.2432432 minutes every hour, which is found to be 0.0540541 of an hour when divided by 60. We multiply this by 9 and then 35 to see that over the week we make a bonus of17.027027. Which is clearly wrong, the answer is 18.

Why didn't the maths workout?
Original post by moomin valley
Yeah so, I've studied towards level 4 maths in the past, but am apparently rusty..
Question:
"A company uses a time-rate method with bonus to pay its direct labour in one of its factories. The time-rate used is £10 per hour and workers are expected to produce 5 units an hour. Any time saved is paid at £9 per hour.
Bob worked for 35 hours last week and produced 185 units.
Calculate the gross wage earned by Bob for the week"
(forget gross, just the bonus calc)
I know there is an easy way to work out the answer, but I don't understand why my method failed and it's really bothering me, thanks.
So I divided 185 by 35 to give 5.2857143 units an hour. Then divided 300 by this number to see the number of minutes it took for 5 units to be produced on average which is 56.7567568 minutes, meaning we save 3.2432432 minutes every hour, which is found to be 0.0540541 of an hour when divided by 60. We multiply this by 9 and then 35 to see that over the week we make a bonus of17.027027. Which is clearly wrong, the answer is 18.
Why didn't the maths workout?

I think you'll find you're saving 3.24... minutes per 56.76... minutes, not per 60 minutes.
Reply 2
Original post by moomin valley
Yeah so, I've studied towards level 4 maths in the past, but am apparently rusty..
Question:
"A company uses a time-rate method with bonus to pay its direct labour in one of its factories. The time-rate used is £10 per hour and workers are expected to produce 5 units an hour. Any time saved is paid at £9 per hour.
Bob worked for 35 hours last week and produced 185 units.
Calculate the gross wage earned by Bob for the week"
(forget gross, just the bonus calc)
I know there is an easy way to work out the answer, but I don't understand why my method failed and it's really bothering me, thanks.
So I divided 185 by 35 to give 5.2857143 units an hour. Then divided 300 by this number to see the number of minutes it took for 5 units to be produced on average which is 56.7567568 minutes, meaning we save 3.2432432 minutes every hour, which is found to be 0.0540541 of an hour when divided by 60. We multiply this by 9 and then 35 to see that over the week we make a bonus of17.027027. Which is clearly wrong, the answer is 18.
Why didn't the maths workout?

this question is simple, you're overcomplicating the method. no minutes should even be involved and nor should any averages.

the question says £9 per hour saved, and each hour is 5 units. so for every 5 extra units you produced above expected you are paid £9.
first we see how much he was expected to make. 5 units per hour, he works for 35 hours.
35 x 5 = 175. he was expected to make 175 units in the 35 hours he worked. however, he produced 10 extra units to get 185. this means he saved two hours.

so then 2 x £9 = £18

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