Question

Solving 8 problems per minute, Fast Finn can finish his test in time. He was however, working faster, solving 10 problems per minutes. That is why he finished 6 minutes early. How many problems were on the test.Solving 8 problems per minute, Fast Finn can finish his test in time. He was however, working faster, solving 10 problems per minutes. That is why he finished 6 minutes early. How many problems were on the test?

Answer 1

Number of problems = 240

Explanation:

Let x be the number of questions and t be the time.

Given:

Average rate = 8 problems per minute

Fast Finn rate = 10 problems per minute

Fast Finn taken time = t - 6

We need to find the number of problems on the test paper.

Solution:

Average rate to solve test paper.

`Average\ rate =(Number\ of\ questions)/(time)`

`8 =(x)/(t)`

`t =(x)/(8)` --------------(1)

Fast Finn rate to solve the test paper.

`Average\ rate =(Number\ of\ questions)/(time)`

`10 =(x)/(t-6)`

Using cross multiplication rule.

`x=10(t-6)`

`x=10t-60`

substitute
`t =(x)/(8)` from equation 1.

`x=10((x)/(8)) -60`

Rearrange the equation as:

`x - (5)/(4)x = -60`

`(4x-5x)/(4)=-60`

`-(x)/(4) = -60`

Using cross multiplication rule.

`x = 60* 4`

x = 240 problems.

Therefore, 240 problems were on the test.