SOLUTION: The time it takes to do homework includes a fixed amount of time to prepare plus a constant amount of time per problem. If a student can do 5 homework problems in 40 minutes, and 1

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Question 269702: The time it takes to do homework includes a fixed amount of time to prepare plus a constant amount of time per problem. If a student can do 5 homework problems in 40 minutes, and 10 problems in 70 minutes, how many minutes will 25 problems take?
Found 3 solutions by mananth, ikleyn, josgarithmetic:
Answer by mananth(16949)   (Show Source):
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The time it takes to do homework includes a fixed amount of time to prepare plus a constant amount of time per problem. If a student can do 5 homework problems in 40 minutes, and 10 problems in 70 minutes, how many minutes will 25 problems take?
Let the fixed time taken be x
The time to solve a problem be y
x+5y=40------------1
x+10y=70-----------2
subtract equation 2 from 1
(x+5y) - (x+10y) = 40-70
x+5y -x-10y = -30
-5y=-30
y=-30/-5
y=4. Time taken to solve each problem is 4 minutes
x+5y=40 substitute the value of y in the equation
x+20=40
x=40-20 = 20 minutes will be the fixed time
25 problems will take (20 minutes + 4 *25)
= 120 minutes or 2 hours

Answer by ikleyn(53742)   (Show Source):
You can put this solution on YOUR website!
.
The time it takes to do homework includes a fixed amount of time to prepare plus a constant amount of time per problem.
If a student can do 5 homework problems in 40 minutes, and 10 problems in 70 minutes, how many minutes will 25 problems
take?
~~~~~~~~~~~~~~~~~~~~~

        Calculations in the post by @mananth are incorrect.
        I came to bring a correct solution.

Let the fixed time taken be x
The time to solve a problem be y
x+5y=40------------1
x+10y=70-----------2
subtract equation 2 from 1
(x+5y) - (x+10y) = 40-70
x+5y -x-10y = -30
-5y = -30
y = -30/-5
y = 6. Time taken to solve each problem is 6 minutes
x + 5y = 40 substitute the value of y in the equation
x + 30 = 40
x = 40-30 = 10 minutes will be the fixed time
25 problems will take (10 minutes + 6 *25)
= 160 minutes or 2 hours and 40 minutes.         ANSWER

Answer by josgarithmetic(39790)   (Show Source):
You can put this solution on YOUR website!
x, how many problems
y, how much time
points (x,y)

Points described are (5,40) and (10,70).

Slope for the linear relationship

Taking point (5,40) and using found slope 6

Finding y if x=25