SOLUTION: the time required to finish a mathematics test varies directly as the number of problems on the test and inversely as the number of hours spent studying. If a 50-problems test can

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Question 30688: the time required to finish a mathematics test varies directly as the number of problems on the test and inversely as the number of hours spent studying. If a 50-problems test can be completed in 2 hours after 3 hours of studying, how long would a 75-problem test take after 4 hours of studying?
Found 2 solutions by Paul, longjonsilver:
Answer by Paul(988) (Show Source):
You can put this solution on YOUR website!

Let the time be x
In first equation:
2x+3x=50
5x=50
x=10
Subsitute it into second equation:
4(10)+10x=75
10x=75-40
10x=35
x=3.5
Hence, it requires a test of 3.5hours.
Paul.

Answer by longjonsilver(2297) (Show Source):
You can put this solution on YOUR website!
the solution by the other tutor is wrong.

Let T = time to finish
let P = number of problems
let H = number of hours of study

we are told 2 things:

T varies directly as P
and
T varies indirectly as H

Mathematically we have T proportinal to , and hence

where k is the constant of proportionality

So first we need to find the value of k, for which the question should supply all other variables:

--> 50k = 6
--> k = 6/50
--> k = 3/25

So, the formula is

Now we can find the unknown, given the 2 values quoted.

--> T = 2.25 Hours
or T = 2 hours 15 minutes

jon.