Question

nutes. 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

Answer:

Number of problems = 240

Step-by-step 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.

$Average\ rate =\frac{Number\ of\ questions}{time}$  

$8 =\frac{x}{t}$

$t =\frac{x}{8}$ --------------(1)

Fast Finn rate to solve the test paper.

$Average\ rate =\frac{Number\ of\ questions}{time}$  

$10 =\frac{x}{t-6}$

Using cross multiplication rule.

$x=10(t-6)$

$x=10t-60$

substitute $t =\frac{x}{8}$  from equation 1.

$x=10(\frac{x}{8}) -60$

Rearrange the equation as:

$x - \frac{5}{4}x = -60$

$\frac{4x-5x}{4}=-60$

$-\frac{x}{4} = -60$

Using cross multiplication rule.

$x = 60\times 4$

x = 240 problems.

Therefore, 240 problems were on the test.