Question

Jack completed 68 math problems in 4 hours. how long will it take him to finish 459 problems

Answer 1

27 Hours

Step-by-step explanation

Step 1

you can easily solve this by using a rule of three,

a) find the proportion

if

jack completed 68 math problems in 4 hours

`\text{proportion}=\frac{68\text{ math problems}}{4\text{ hours}}=17\frac{problems}{\text{hour}}`

Now, we have the proportion "the speed" of Jack.

Step 2

Let

x represents the time to finish 459 problems, the proportion is the same, so

`\begin{gathered} 17\frac{problems}{\text{hour}}=\frac{459\text{ problems}}{x} \\ 17=(459)/(x) \end{gathered}`

Step 3

finally, solve for x

`\begin{gathered} 17=(459)/(x) \\ \text{Multiply both sides by x} \\ 17x=x\cdot(459)/(x) \\ 17x=459 \\ \text{Divide boths dies by 17} \\ (17x)/(17)=(459)/(17) \\ x\text{=}27 \end{gathered}`

so, the answer is 27 hours