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.



 

RELATED QUESTIONS

Translate each statement into a mathematical statement. Use k as the constant of... (answered by Cromlix)

Suppose that it takes 9 hours for four workers to roof a house. If the time required to... (answered by ankor@dixie-net.com)

Using k as the constant of variation, write the equation of variation for each following.
 (answered by mananth)

If x varies directly as t and t varies inversely as the square of y, what is the... (answered by ankor@dixie-net.com,josgarithmetic)

the time required for an elevator to lift a weight varies directly with the weight and... (answered by Cromlix)

If x varies directly as t and t varies inversely as the square of y, what is the... (answered by josgarithmetic)

The number of correctly answered test questions varies directly as the number of... (answered by 303795)

Hello can I please get help for these 3 problems:
Problem 1: The score S on a Math 012... (answered by ikleyn)

The time required to complete a job varies inversely as the number of people working. It... (answered by fractalier)