Question

When Mei does 17 push-ups and 6 sit-ups, it takes a total of 35 seconds. In comparison, she needs 41 seconds to do 20 push-ups and 7 sit-ups. How long does it take Mei to do each kind of exercise?

Answer 1

It takes 1 seconds for push-ups and 3 seconds for sit-ups for Mei to do exercise.

Explanation:

Given:

Let the time taken for push-ups be 'x'.

Let the time taken for sit-ups be 'y'.

Now Given:

17 push-ups and 6 sit-ups, it takes a total of 35 seconds.

So we can say that;

`17x+6y=35 \ \ \ \ equation \ 1`

Also Given:

41 seconds to do 20 push-ups and 7 sit-ups.

so we can say that;

`20x+7y=41 \ \ \ \ equation \ 2`

Now Multiplying equation 1 by 7 we get;

`7(17x+6y)=35*7\\\\119x+42y= 245 \ \ \ \ equation \ 3`

Now Multiplying equation 2 by 6 we get;

`6(20x+7y)=41*6\\\\120x+42y = 246 \ \ \ \ equation\ 4`

Now Subtracting equation 3 from equation 4 we get;

`120x+42y-(119x+42y)=246-245\\\\120x+42y-119x-42y=1\\\\x=1\ sec`

Now substituting the value of x in equation 1 we get;

`17x+6y=35\\\\17*1+6y=35\\\\17+6y=35\\\\6y=35-17\\\\6y= 18\\\\y=\frac{18}6 = 3\ seconds`

Hence It takes 1 seconds for push-ups and 3 seconds for sit-ups for Mei to do exercise.