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.
[tex]Average\ rate =\frac{Number\ of\ questions}{time}[/tex]
[tex]8 =\frac{x}{t}[/tex]
[tex]t =\frac{x}{8}[/tex] --------------(1)
Fast Finn rate to solve the test paper.
[tex]Average\ rate =\frac{Number\ of\ questions}{time}[/tex]
[tex]10 =\frac{x}{t-6}[/tex]
Using cross multiplication rule.
[tex]x=10(t-6)[/tex]
[tex]x=10t-60[/tex]
substitute [tex]t =\frac{x}{8}[/tex] from equation 1.
[tex]x=10(\frac{x}{8}) -60[/tex]
Rearrange the equation as:
[tex]x - \frac{5}{4}x = -60[/tex]
[tex]\frac{4x-5x}{4}=-60[/tex]
[tex]-\frac{x}{4} = -60[/tex]
Using cross multiplication rule.
[tex]x = 60\times 4[/tex]
x = 240 problems.
Therefore, 240 problems were on the test.
