Question

The amount a gardener gets paid is directly proportional to the number of hours it takes for him to complete the job.

the gardener got paid £70 for a 12 hour job.
how much would he get paid for a job that took a total of 18 hours?

Answer 1

£105

Explanation:

The pay is proportional to the time, so working 18/12 = 3/2 times as long will gain the gardener 3/2 times the pay:

3/2 × £70 = £105

He would get paid £105 for an 18-hour job.

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Here are a couple of other solution methods.

as a proportion

pay/hours = ?/(18 hours) = £70/(12 hours)

Multiplying by 18 hours, we get ...

? = £70×(18 hours)/(12 hours) = £70×(18/12)

? = £105 . . . . pay for 18 hours

He would get paid £105 for 18 hours.

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as direct proportion equation

The equation for a directly proportional relationship is ...

y = kx

If we let y represent pay and x represent hours, then we have ...

70 = k(12) ⇒ k = 70/12 = 35/6

Then for 18 hours, the pay is ...

y = (35/6)x

y = (35/6)(18) = 35(3) = 105

He would get paid £105 for 18 hours.